I finished Fallout 2 by the reactor meltdown. When I left the oil rig, the game ends there. There is an ending that allows me to continue playing after killing Frank Horrigan, right? What is it and how can I do it?

well im not sure Ive never even made it to the oil rig. i always end up in a spot where i cant win and i have to restart. like sleeping with Mrs Bishop,or going on a shooting rampage in NCR.but here check this link maybe you'll find what you looking for
[link name=look here]http://user.tninet.se/~jyg699a/fallout2.html [/link]

Well, you ARE supposed to be able to play for 13 years of game time, though things don't work so well after about six years. As a matter of fact, many of the people in 'the world' have different dialog for you after the end. There are also some new things to do in New Reno and Vault City. Normally after the battle with Horrigan is complete you should be able to leave that map and end up back on the tanker, though Horrigan might have perma-closed some of the doors. If you aren't able to leave then your game probably needs to be patched. The best official patch is version 1.02; i recommend an unofficial patch by 'killap' that fixes several areas of broken-ness in the game.