Luckily, we could handle this for a goodly while if we had to. I would hate to be in your shoes because there simply aren't any good answers.
It sounds like a month or two's grace would not break the bank, and being a decent human being is it's own reward. You'll sleep better for delaying FIRE for a month or three. Decide what you can afford, double check that against the local laws so you don't get a multi-month delay as a surprise, and communicate that clearly to them, in writing. They aren't going to be at their best, so take pains to be extra clear.
If it comes time for them to move out, help them move. If they're both in the hospital or nursing home, rent them a storage unit and help them by moving their stuff to storage instead of tossing it out to the street. You can hire folks to help move via UHaul.
Now, if these folks were just scum-sucking grifters who were in the habit and mindset to cheat their landlords (and anyone else), I would say file the paperwork to evict first thing in the morning.
Best of luck.