Is there anything that can be done to convince parents to cut back on the number of cats they feed, home, and care for?

That (waiting for the catastrophe) is often the case regardless of the compulsion or addiction.
Perhaps in your area there is an agency that will take on the cats? You didn’t indicate that they were endangered in any way. Regardless they might help relocate the cats. It seems like it would be beneficial to at least know the options before that catastrophe occurs in order to take the cats quickly.
I know this must be a very stresssful problem for all concerned. Good luck and let us know how things go.

Are your parents running a cat shelter? You said cats are their life. Not having the cats, to them, would mean not having a purpose for living. I hope the cats are neutered and spayed so they don't multiply even more. Perhaps, you can look for an organization or several that can help rehome some of the cats, leaving your parents just enough so that they can continue caring and not go bankrupt in the process. I hope they are still of sound minds that they will understand and let you help.

On a positive note, at least they are not actually living among the cats. This is known as animal hoarding and like any kind of hoarding is a complex problem, the ASPCA has several articles you may want to read.

I agree with CW - try tackling this from a cat welfare point of view. Enlist the support of animal welfare organisations. Your mother may listen to them far more attentively than she would to anyone concerned about her.

SPCA - call them.

Thank you for your suggestions. I have been in contact with a few organizations regarding the cats. Two of them may be able to help rehome them, if the parents willingly give them up. Maybe my previous post was unclear, they do have more cats in their home than what most people would consider "normal." I understand they love the cats and see them as their own children. So I'm trying to be careful, sensitive, and loving. But at the same time with Dad being very ill, his immune system is compromised, so that's also another concern. In addition, there are children and grandchildren that want to (have wanted for years) be a part of the parents' / grandparents' lives, and they claim they want that too, but then isolate themselves & don't answer the phone. Our mother spends a good part of days taking care of the cats and the business.

I'd call Animal Control and see if you can report them for cat hoarding.

In my Township you are only allowed five animals a home. I would tread lightly when it comes to calling in Animal Welfare and the SPCA. You need to check to see if both have or make sure cats are going to no kill shelters. My County has a no kill shelter but is limited by law to how many cats and dogs can be at shelter at any one time. They foster a lot. Maybe you can have someone come to talk to them about it's not healthy for them or the cats. It would be nice if the cats could find loving homes.