Bronson is, quite simply, a drunk. Unable to cope with life since his capture, he's taken to humiliating himself for the amusement of the slavers, who provide him with enough booze to make him forget how his life has ended up. Bleak has been trying to give him hope, but so far has failed.
Bronson is locked up in the Paradise Falls slave pen, spending his entire life there until he is killed or has escaped.
Rescue from Paradise: If you disable the collars and unlock the slave pen you can convince him to leave. You can choose to tell him he can have "all the booze he wants on the outside", which he promptly agrees to and leaves.
When first interacting with him, he offers to show you something funny, or asks if you wish to hear a song or a dance, but only in exchange for booze. However, the player cannot give any alcohol and therefore cannot exchange booze for anything.