San Diego was rumored to be in on Despaigne in early April. He's pitched eight years in Cuba with a career 3.65 ERA; he is projected to be a back-end starter or a bullpen. Despaigne was signed to a minor-league deal worth $1 million.
In exchange, Houston will receive either a PTBNL or cash. The Braves faced him once in 2012 and he beat them, but he's always had trouble with walks (200 in 401.2 innings). If not even the Astros want you, then you must be doing pretty bad.
Hanrahan is coming off Tommy John surgery in 2013 and has put together a decent, but not great, career. In his two years as closer, he's only been so-so and with him recovering from surgery, the Tigers are taking a big risk.
I'm not one to celebrate a person's injury, and he's only diagnosed as day-to-day, but I can't say I feel sorry for him.