OK,so during the Fallout 1's quest to kill the high priestess Jain the game will crash after I kill her.

By the way,the game left that black square.

I am not familiar with this problem, and seemingly neither does google.

Basic Troubleshooting though, reinstall the game - it is all you can do unless someone know how to fix it and hasn't spoken up :)

If you have companions, try dismissing them before completing the quest and see if that makes a difference.

Good idea.