Buck Broke is the father of Trigger Broke and Susie Broke, as well as the widower of Mary Lu Broke. He is the brother of Flat Broke, and uncle of Skip Broke and Ruby Broke. So far, not much is known about him since he was not mentioned in either the The Sims, or the The Sims 2. His name is a pun on Buck as in dollar and Broke as in poor as he lives in a very poor family due to them having low paid jobs. He works at the Old Town Cemetery as a Mausoleum Clerk although this isn't inline with his lifetime wish. In order to complete it, he must be employed in the music career.
The age gap between Buck and Flat is so great that Buck is closer in age to his niece than to his brother. Buck's age is inconsistent with that of his son, Trigger. Buck is technically too young to have a teenage son and him and Mary Lu would have had to have been teenagers when they had Trigger for this to be possible but it isn't possible in the base game.