I am trying to find a short story I must have read about 30 years ago. People who have committed very serious crimes are given the choice between permanent incarceration and having an implant where they are permanently controlled by aliens. I think the premise was that whilst there was FTL communication it did not support travel, and the different species of aliens would use their criminal hosts to attend trade conferences etc. The protagonist had a girl friend who was also controlled and sometimes they would be given minutes off to be with each other. I can't remember what happened at the end.
I'm reasonably sure this is We Purchased People by Frederik Pohl.
The controlled people are called "purchased people". The protagonist and the woman he is in love with are both purchased.
At the end
The purchasers make the two of them have sex- "...those freaks who owned me did to Carolyn with my body all manner of things and I could not even cry." (she dies) and the protagonist suffers a breakdown "It was discovered that when control was withdrawn he became destructive, both to himself and others." Apparently the crime of the protagonist was that he was a sex-killer, and the aliens made him kill her out of a sort of misunderstanding. "..the sexual behavior which had been established as his norm - the destruction of the sexual partner - may not have been appropriate in the conditions obtaining at the time of the experimental procedure."
It's one of Pohl's darker stories.