Notice! You can complete this mission only after finishing Cleansing the Stones!
On the main square of Raven Rock you will come across a Dunmer named Bralsa Drel. The woman was once a skilled miner, but she started drinking and she went downhill. What's worse, Geldis Sadri - the owner of the nearby tavern The Retching Netch - doesn't let her drink inside his property.
If you were touched by the story of the Elf-drunk, you can try convincing the bartender to let her back.
He will tell you that Bralsa used to be the wealthiest person in town - unfortunately, she spent everything she had over the years on alcohol. Geldis is convinced that if she stops drinking, the will become a better person. Unfortunately you have your interest in her returning to her addiction. That's why you have to either intimidate, convince or bribe the man and therefore complete the mission. There's no way of supporting the bartender in his noble cause - you can complete the mission only by making Bralsa welcomed at Geldis' inn again.
Tell Bralsa Drel she's welcome at the Retching Netch
Since you have already persuaded Geldis to let Bralsa drink till passes out (you bastard!), return to her to collect your prize. It's generated randomly - you will obtain a useful item depending on your character's level.
Next time you come across a drunk Bralsa, you should think about your behaviour.