Evict the widow

 is an unmarked quest in Fallout 2.

Quick walkthrough
Widow Rooney is an impoverished woman, and Mayor Ascorti wants her to be evicted. If the Chosen One decides to help Sheriff Marion with his duties, they will be forced to deal with the widow problem - either by paying her rent (120$) or kicking the old crone out.

Detailed walkthrough
The widow is in the small shack with the brahmin pen just southwest of the sheriff's office. If you go talk to her about her plight you can either kick her out like the sheriff told you, or you can pay the $120 of back rent she owes. If you pay the back rent you receive 1500 experience as your reward. You also get paid $100 by the sheriff for completing the task so the net cost is only $20.