Should I be worried I might get fired while searching for new job?

So I plan to leave my job soon and I want to go ahead and have another job lined up for when I leave. But I don’t want my current employer to figure out I’m looking for a new job incase he may fire me for doing so. Is that a normal thing that happens? Do most companies you apply to not reach out to current employers while your still working there? Or is there a chance they may reach out and accident let your boss know you are thinking of leaving?

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