It's always interesting when this happens. In the short term it sounds like the Sheriff's department will simply assume the duties of the city police, which could always be the long-term solution as well provided the Sheriff can obtain the necessary resources. If the city government is corrupt, as it sounds like it might be, having the county take over law enforcement might be a good idea.
This seems like a radical act, but in fact it's come up a number of times before. Typically chaos does not result. Americans have a long tradition of self-governance, and overlapping institutions (one of the characteristics of an anti-fragile system), which means that these cases are more opportunities for reform than disasters waiting to happen.