There's always this common reference in some TV shows but is it really possible?
People often don't realize that even soldiers "hiding out in foxholes" still receive regular resupply and communication from their commanding units. It's rare for individual soldiers to be completely isolated from their chain of command for more than a few days.
Even in World War 1, yeah, there would be trenches manned for years at a time, but individual soldiers might only spend a couple weeks or a month in the trenches before being pulled back to be replaced by fresh men.
The only way I could really think this might happen is with maybe an isolated island with troops on it that was simply forgotten about in the shuffle of paperwork at the end of a war, but that's still unlikely.
This sounds like a WWII reference to Japanese soldiers on Pacific islands. There are a few comments in these posts
... and just because I ran into these, a couple on soldiers in Europe
No, it wouldn't be possible. It's definitely unheard of and wouldn't rationally make sense considering how the war was carried out of a VC perspective. Perhaps if you could provide me with some of the TV references (which I've never heard myself), I can break it down for you more easily?