Yes, this is definitely possible in the game... and actually allows you to play (almost) indefinitely!
So, yes... not only Fallout 2 has an unlimited gameplay after ending the game!
(well, almost unlimited - there's an end screen in F2 after 13 years ; )
There is a rumour that also Fallout 1 has also such an end screen, but so far this has been unverified. If I recall correctly, there are still some hard limits on game ending, even in the latest version (earliest versions had the mutant army attacking and ending the game after 500 days, this value was also affected by making a trade with water merchants in the Hub).
To achieve a successful escape from the last cave (Cave Story, anyone? ; ), definitely some luck is needed, as even pressing no keys can lead to Jacoren, the overseer, to appear. Once the control of the character is regained after finishing both of the main quests (and being brought back to the starting cave), one must run away like hell (speedclicks to the south exit) from the immediate whereabouts of overseen spawn. Further down the corridor we'll be out of his sight and he won't bother us anymore... and we can roam the wastelands freely and happily.
That is, UNLESS we decide to return to Vault 13, thus potentially ending the game.
Talking to Jacoren triggers the very same dialogue he would normally throw us out with in the cave, but it happens... right inside the Vault, on its 3rd floor, right next to his pedestal.
Naturally, in the optimistic scenario (as I like to call it: LANparty @ Vault 13 :D) instead of throwing us out, the whole Vault throws a giant LAN party, using all of the computers to play multiplayer games instead of some unimportant science stuff ; ). Everybody, even the overseer, join the party, they have pizza, coke and balloons. Aaand they lived happily ever after ; )
Fin.
:D
PS.
But the Chosen One has left the Vault because of the disappointment in other players' skill.
n00bs.
PPS.
More antics coming slowly : )
0:00 Game ending stills
0:12 Runaway from the cave 13
0:25 Return to Vault 13 (just for the kicks of it)
0:38 Way too much fun with skipping of the door animation
1:10 On the way to talk to the old bastard
1:22 All important quests completed... who needs water ;)
1:47 FALLOUT 1 ALTERNATIVE ENDING: LANPARTY @ Vault 13 : D