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tl;dr - It's not the word you think it is

Short answer: the "for" isn't a preposition, it's part of the verb "to do for", it doesn't have any meaning on its own, and the reason why that word and not another are lost in the mists of time - if there ever was a reason.

Phrasal verbs

"To do for" is an example of what's known as a phrasal verb in English. The verb is to do for, and it's transitive (i.e., it takes a subject, so you have to say "to do for (object)"). This can look confusing if you try to analyse it as the construction "to do (X) for (Y)", but in that case the verb is simply "do", and "for" is acting in its normal role as preposition.

The closest synonym for "to do for" is to doom, although many of the common uses can also carry the meaning of "to kill". "To do for" is quite informal, though - you won't see this in a coroner's report, but you will often hear people on the street using it (e.g. "It was the drink that did for him in the end", or "He did for my shin with that last tackle!").

As you note, "We are done for" is simply the passive-voice version of the active sentence "(someone) has done for us", meaning that someone has doomed us to a fate, although that fate does not have to be death. It's almost a stock-phrase, and it's slightly comedic: this phrase is often uttered by villains in British comedy writing - there it is best translated as "all is lost, and we will be caught and imprisoned".

"Do for" is used in its active sense, but very rarely in American English. I have heard British speakers saying things like "I did for my leg last night" meaning that they've injured themselves, but it's very much informal, and it may be regional (North of England rather than South).

The bits don't mean anything on their own

Some advice: do not try to look for some kind of deeper meaning behind the two parts of this kind of verb. Some make sense ("take in", "drop off", "run out"), but others don't really ("do in", "let on", "give up", "turn up"). Just accept that in English, there are some verbs that are made up of a "verby" word and a "prepositiony" word that act together to create a completely new, and usually idiomatic, meaning.

( This isn't just English, by the way. German has many such idiomatic phrasal verbs such as umbringen. That one looks like it should mean "bring around", from "um" and "bringen", but it actually means "to kill" - however, the sentence "ich bringe die Kinder um 08:00" doesn't mean you're planning a murder!)

Here are some other common phrasal verbs of the same type as "do for":

• I give in : I admit defeat


• She gave out about... : (first meaning) She complained about...


• The bearing gave out : (second meaning) The bearing failed


• I give up : I quit


• I did in my knee : (informal) I damaged my knee


• I did up the room : I decorated the room


• She turned up today : she appeared today


• She turned down the invitation : she declined the invitation


• She had a grey dress on : She wore a grey dress

My personal experience (I speak British English, but work extensively with Americans) would suggest that there are more of these verbs in regular use in British English than American, but they're a common feature of English, and they're not something you can avoid.

According to Green’s Dictionary of Slang done for is the adjectival form of the phrasal verb do (a bad turn) for meaning to injure, kill. The preposition for would derive from the verbal form.

Done for adj.

(do for v./ext. of done adj.)

1821:
without a chance, hopeless, defeated, lost, abandoned, ‘finished’.

• 1843 [UK] ‘Bill Truck’ Man o’ War’s Man - 112: He’s done for now,
  

Do for verb:

[Do v.1 (1)/abbr. SE phr. do a bad turn for

to beat up, to injure, to murder.

• 1751 [UK] Fielding Amelia II 70: He said something, too, about my master [...] he said he would do for him, I am sure he said that; and other wicked, bad words, too.
  

The meaning of "done for" here cannot be found by combining meanings of "done" and "for" somehow.

done for
PHRASE
informal

In a situation so bad that it is impossible to get out.

‘if the guard sees us, we're done for’

Oxford Dictionaries

The for in to do for is acting as part of a phrasal verb, not a separate preposition.

English has the concept of phrasal verbs, which is taking a verb and combining it with an adverb or a preposition to create a new verb. This new verb loses the meanings of its individual parts and takes on a brand new meaning of its own.

A simple example is the verb to pick up. Compare the following sentences.

1. Did you pick this ball?


2. Did you pick up this ball?

The first sentence has a clearly different meaning from the second.

Your example works the same way. The verb to do is clearly different from the verb to do for. The second sentence may sound weird because of the archaic nature of that form, but it's basically the same as above.

1. Did you do her?


2. Did you do for her?

Again, the first sentence has a clearly different meaning from the second.

To sum up, the for in your example does not have a separate and distinct meaning. Instead, it changes the the verb to do to a different verb to do for that as a whole has its own meaning.

A more thorough explanation and several other examples of phrasal verbs, may be found here: https://www.englishclub.com/grammar/phrasal-verbs.htm

In colloquial usage, "to do for someone" can mean "to perform a service for" them, especially as an actual servant.

If the service was done in the past, you could say "Someone is one who has been done for," which can be shortened to "Someone is done for."

If the service hasn't been performed yet but is considered inevitable, the person is "as good as done for or simply done for.

In your question, "to do for someone" is ironic. The "service" to be performed is to kill them or thwart their intentions and it's definitely (in the speaker's opinion) going to happen. "He doesn't know it yet, but he's a walking dead man."

In any case, "someone" is the implied object of the preposition "for." No mystery there.

The idiomatic expressions "done for" means finished in the sense of defeated or killed and the precise meaning depends on the context. Idiomatic expressions in English cannot be interpreted or explained grammatically. The preposition "for" usually takes an object but in this case the expression is a synonym. I have never heard it used in another context such for example in the sentence "Bill did for him" or "Team A did for team B". "Done for" is a colloquialism.

Some food for thought of where this might come from

Done is the past form of do

Middle English do, first person singular of Old English don "make,
act, perform, cause; to put, to place," from West Germanic *don (cf.
Old Saxon duan , Old Frisian dua , Dutch doen , Old High German tuon ,
German tun ), from PIE root *dhe- "to put, place, do, make" (see
factitious).

- https://www.dictionary.com/browse/do

While for as a prefix has the meaning

a prefix meaning “away,” “off,” “to the uttermost,” “extremely,”
“wrongly,” or imparting a negative or privative force, occurring in
verbs and nouns formed from verbs of Old or Middle English origin,
many of which are now obsolete or archaic:

- https://www.dictionary.com/browse/for?s=t

So from this, the rough translation of "done for" to "have been made away" may be related or have come from it's old-english/germanic roots.

To "do" is to make death certain.

So to "do for" somebody, is to make death certain, for them.

So it's the meaning "pertaining to, or affecting".

The O.E.D. gives 12 definitions of the word 'for' in the link you posted (the American dictionary page linked to gives many more, but I lost the will to live after the first three dozen, so let's just stick to the O.E.D. for now).

The answer is easy: none of the 12 definitions listed is appropriate for the word 'for' in the context you've cited ('done for').

The O.E.D. is mostly only listing definitions of the word that fulfill some kind of counting function ('for 300 yards', 'for 12 years', 'for £1.20', 'for the 3rd time', '2 bottles for your 1') or some form of possession (it lists objects, persons and feelings belonging to someone: 'you', 'Napoleon', 'everyone', 'the department', 'the Open University', 'her family').

Significantly, it gives a dozen definitions - all of which have some merit as independent, separate meanings of the word, in various contexts.

The significance, to my mind, is that there are so many definitions: perhaps more than for any other word in the dictionary. And that, even so, the list given does not cover the usage you are citing (in 'done for').

This suggests, to me, that the word 'for', by reason of its extreme antiquity, deriving from the Anglo-Saxon roots of the English language (reference has been made to it being used in c.900 AD), only has a meaning in context. Or perhaps one should say, it has so many meanings - due to its antiquity - because it has acquired its meaning from its context (unlike most words, which can generally be understood apart from any context).

Short words of Anglo-Saxon origin (for, of, at) tend to be inordinately flexible in meaning and usage. It suggests that these are words which the language built up around. They have no invariant meaning, and only acquire meaning from the context. There is, accordingly, more truth than you suspected in your remark that 'most prepositions have so many meanings'.

Most words have multiple meanings, and those which have been around the longest have acquired the most. No word ever came 'pre-defined', all words originally acquired their meaning from their context. But there are few words you could have chosen which would have made that point more clearly than this one.

In the context you've specified, the word 'for' can only mean doomed. It can't possibly mean anything else. Yet the O.E.D. gives it 12 different meanings, in 12 different contexts, none of them remotely similar to this. The implication is that one could go on, indefinitely, citing examples of this word in different contexts. The O.E.D. doesn't attempt that. Dictionaries have limitations. Languages don't.