True, the Empire would raise the bounty for such a Wookiee, just to make sure that he got put down. The longer he is on the run the more charges he will rake up, like assaulting law enforcement, private citizens, property damage, smuggling, illegal posession of a firearm, ... just to name a few.
If the bounty is too low to attract (good) bounty hunters than the Imperial Navy/Army will deal with him. And if they fail ... well, see charges above.
After a few run-ins with the Imps the bounty will go up.
I'm kinda repeating myself here.