Can the post office claim your money if they go bust?

The question as asked makes no sense.

I'm assuming the question you're trying to ask is something along the lines of "I have a postal money order; if the post office goes bankrupt, what happens to my money?"

The answer is that it probably gets distributed to other creditors. If you attempt to assert your own claim in the bankruptcy hearings, then you might get (some) of the value of the money order.

This is all extremely silly, though, since money orders are a stupid place to keep money (they're intended for short transactions), so there's no reason to hold onto them instead of immediately claiming the money so you can quit worrying about it.