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Koboro Station, in rural Hokkaido, is a famously remote train station. According to Hokkaido Likers, Koboro train station on the Muoran Line "cannot be reached by car" and further states that the "place cannot be reached except train" [sic]. It implies that you can, however, travel to a nearby temple from the station.

Is Koboro Station accessible by foot from anywhere else in Japan? If I look at Google Maps, I see a dotted line that leads from the station to the beach, and in the other direction, close to a parking lot next to the Tanshin National Highway, but it is unclear if there is an actual navigable walking path. I looked at walking along the shore, but, per Google Maps, that shoreline looks pretty rocky and precarious.

The dotted line you see on Google Maps is the administrative border between the districts Yamakoshi and Abuta.

Looking at other maps of the region, there is however a foot path from the station to the beach and to the Buddhist temple. If you look at Google Maps, there are several photo spheres along this path, and it seems easily walkable. I can find no foot path on the maps from the station to the nearby parking lot you are mentioning, but the distance is only about 400m and there are no obvious obstacles on the maps or on the aerial photos of the area, so I would assume that it is feasible to walk through the forest, even if there is no marked foot path there. On the Google Maps images from the station area, you can find a clearing in the forest in the right direction.

The town of Toyoura has an information page about the nearby Buddhist temple, Iwayakannon. It says that the temple is accessible by boat or by foot from Koboro station. That seems to confirm, that there is at least no 'official' foot path from the station up to the road or parking lot.

That's actually quite common.

There are stations on the Welsh Highland Railway and Algoma Central that are also accessible only by rail. Many cabins along the Algoma Central are accessible only by rail or floatplane, and the train makes a flagstop for those patrons.

Tourist railways have been known to have "stations" in the middle of nowhere, either as a turnaround point, scenic overlook, or hiking/picnicking destination - such as the Cass Scenic Railroad's Bald Knob.

For many of these, rubber-tired-vehicle access may be possible if you have a high clearance vehicle like a Jeep, don't mind driving overgrown fire trails, and have all the right keys to various locked gates. There's a fair chance the local fire department knows how to get there. But such a path was never imagined for general public access with street vehicles. Does this count as "cannot be reached by car"?

And once you open the door to non-revenue "stations", e.g. a maintenance of way depot, then they are common (for anti-theft reasons among others). Most spectacularly, the Gotthard Tunnel's Sedrun station, which had been proposed to be a revenue station to connect to the narrow-gauge above, via a rather tall elevator.