I don't think these communities go without a police force. The name is changed the dispatch point may be changed, but...
From what I have seen, and admittedly, it ain't much. Dropping a police force has huge financial benefits to some communities. Think about all the savings.
Re-negotiate every contract, and start from scratch, too. Hourly rate, med coverage, all of it is now up for grabs.
Remove all seniority from the payscale, again all new hires.
Everyone starts with a year without vacation pay, then next year one possibly two weeks.
No more public pension, fund a 401k, at whatever level is chosen.
Quite possibly the union will be eliminated too if that is an issue.
The County Sherriffs office goes from twenty-five deputies who largly hande court work and rural enforcement to 400 deputies who are now patroling city streets. Likely they occupy the same jail and facilities the old city force did (leased from the city?), hell many of the same officers too. As new hires they don't have the bennies they once had ( and that certainly sucks ), but the Sherriff is at fault not you the city manager, your hands are clean of that problem.
The savings add up pretty fast. If you are tasked by the community with staying within budget the appeal is obvious. Write a monthly check to the county for policing of the community and you are done. No future liabilities no administrative cost in either time or money or headaches.