Most people are employees at will and have no employment contracts or union contracts that protect them. That means that a boss can fire them at will for any legal reason (that carves out such things such as race, color, creed, etc.) or no reason at all. If there is an employment contract, or a union, that's different.
Most bosses aren't stupid enough to do random firings as it can be horrible for morale. Also, most large companies have rules that their local managers are told to comply with, that are designed to prevent arbitrary firings as senior managements know that it is bad for business long term. But insubordination is always one ground that is open. You can comply or appeal to higher management, but my guess is that if push comes to shove, you'd be out, not the boss.
the boss is asking you to reveal what you regard as a confidence. Whether that is wise or not, I can't say as it depends on the circumstances, and whether the boss has reasonable grounds for suspicion related to the business' needs, or is just being nosy. The boss must look after the needs of the business first. But you better make a case as to why the information should not be given (it did not concern the business but a personal matter about her sister in law who lives in Denver), lie about it (she said she was looking for another job to you but you tell the boss she was telling you about her ex-husband -- but if the boss finds out he'd fire you for lying), try to disguise it (she said she was not happy dealing with some of the customers here, when she actually said she was afraid to work the late shift) or begin to look for another job.
ven, lie about it or
