Most police officers in this country are subject to specific labor law, which precludes police officers from striking. Offhand, you wouldn't think that a municipality would even need a law like this on the books, because if police office believe that their self-interest is greater than the community's self-interest, one could very well question their loyalty to their given community to begin with, as after all, for instance, uniformed soldiers, do not have the option of only obeying and doing the things that they so desire, and cannot thereby ignorerules or commands that don't suit them, or if they do, the consequences of such an action are rather tragic.
Nevertheless, from time-to-time, police officers have gone on strike, or, have played a game of massive call-ins of sickness, or the reluctance to perform their given, daily duties, all to assert pressure on communities, to give in to their demands, legitimate or not. These types of behaviors by the officers, themselves, are seldom justified, no matter the circumstances, because all officers have a duty to uphold the legitimacy of the state, and to thereby taking "the law" into their own hands is a definite dereliction of duty.
That said, since there have been strikes of police officers in municipalities as well as sick-ins, one might wonder as to whether or not, communities quickly degenerate into total chaos and anarchy when the "cat is away". The quick answer is no, for a lot of reasons, of which one of them is, that the citizens of America are capable in extreme situations of policing themselves, fairly effectively, as not only do they have the desire to do so, they also have the wherewithal to do so, as no nation has more citizens that are armed. In practicality, though, communities that are suffering from a police strike or strike-like actions, are quick to call upon State militia, militia in general, the National guard, Federal troops, and so forth, so as to make clear to the criminal elements throughout a community, that though the "first team", may not be in action, that the backup is quite capable of doing what is necessary to maintain order.
In point of fact, in an era in which many police officers don't know their communities or have little interest in doing so, that police officers have, in essence, marginalized themselves, because if policing is done more and more, by computer processing power and analytics, and less and less by engaging with the people in a mission to actually protect and serve, than a "cookie cutter" replacement, specifically, those that are active duty servicemen and servicewomen, could, in a time of crisis, probably fulfill the duties of policing activity in communities rather well.
When agents of the state, aggrandize unto themselves, that they are bigger or a more important part of the state, the state, will, always, crush that incipient revolt, sometimes with a velvet glove, or sometimes with an iron fist, but make no mistake, those police officers that believe that without their patrolling and police duty work, that communities would unravel into complete chaos in a short period of time, are badly mistaken, which is a significant reason why there are so few strikes.