But if you buy a 3rd party lens then theoretically it could stop working tomorrow.

Only if you try to use it with a camera model newer than the third party lens. If it worked with your camera when you first got it, it should continue to work with that camera. There's really no additional risk that it will suddenly stop working with a camera with which it currently works. Where the compatibility issues come in is when the camera maker introduces newer camera models that weren't available when the 3rd party lens company developed their lens.

That means that if you buy a 1st party lens, it's guaranteed to work with your camera.

Not necessarily, even though the risk is certainly much, much lower. But it does occasionally happen with first party lenses. When Canon introduced the 7D Mark II there was an initial compatibility issue with AF at focal lengths of around 100-130mm with the EF 70-200mm f/2.8 L IS II. Canon issued a firmware update for the 7D Mark II a few weeks later that fixed the issue.

In reality, how common is it for a 3rd party lens to quit working due to an incompatibility? Is this a common problem or just a theoretical possibility? If your favourite 3rd party lens suddenly stops working, what can you do about it? Is the lens manufacturer going to care, or do you just have to toss the lens in the bin and go buy something else?

It seems you are assuming that a third party lens model can just spontaneously stop working with the same cameras with which it has previously worked. That is not the risk of buying a third party lens. I guess it's possible a firmware update to the camera could theoretically cause issues with a third party lens that previously was fully functional, but I've never encountered such a situation. The issue is usually only seen when trying to use an existing third party lens with a newly introduced camera model that wasn't available when the lens was being designed. Such lenses will continue to work with the cameras with which they previously worked.

Lens manufacturers, including third party makers, will vary with how much they stand behind and support their lenses. The two or three largest names in the third party lens market tend to support them very well. In the past firmware updates would often be made available but required a trip to a service center to be applied to the lens. Often these were offered at no or very little cost for a specified time period after issues were discovered and corrected through a firmware update.

Recently, though, Sigma and now Tamron have developed hardware docks and made them available to end users so that the firmware running in lenses can be updated by the owner without having to send the lens off to the manufacturer's service facility. It's as simple as downloading the updated firmware and using a USB dock to load it onto your lens.