Maywood, CA actually laid off ALL of its city employees and outsourced EVERYTHING - police, crossing guards, firefighters, all of it. Some of it they just pay other towns to do it for them, and others they hired private companies. Supposedly, it's working wonderfully.
While on the one hand this is bizarre, on the other hand, it's actually kind of heartening. Instead of being stuck with crappy bureaucracies, if another town or a private company is able to offer the same level of police coverage for less, or better coverage, then the town can switch. In effect, they're making use of competition to improve city services beyond what they were capable of doing internally. It's brilliant, and I wish more towns would look at the model.