This can certainly happen but it's definitely uncommon bordering on rare, especially for folks who keep paying (or with whom you're willing to work out a deal). And running credit and background checks on prospective renters goes a long way toward eliminating folks who are going to be prone to stop paying a lease halfway through.

Things happen. People lose their jobs and according to most banking standards, they expect a 75% occupancy rate when considering rental income.

It only takes one bad tenant who doesn't pay for 3 months over 3 or four years and repair costs to wipe out all of your profit.

Mortgage insurance. It's requires for my FHA loan, but I've also paid 3 months ahead on my mortgage to give me additional breathing room.

Mortgage insurance doesn't protect you, it protects the bank. The bank can still foreclose just as fast, they are just guaranteed to get their money if the price they sell the home for is less than the amount you owe.

But it still only takes one bad tenant or one good tenant that comes on hard times to cause you to lose all of the profit.

Isn't there insurance for this exact kind of thing?

Insurance for vacancies and dealing with non paying tenants -- no.