The pictures are fuzzy so this is hard to tell, but your plant might be a Mammillaria elongata. You have obviously had this plant a long time because it has many stems. It also appears that your plant has had a chronic lack of light, at least in recent time.

The fuzz makes it hard to diagnose well, but if some of your stems are healthy you can cut off pieces, let them heal over, and root them independently.

When was the last time you re-potted it into new soil, and how do you fertilize it? It loks like it's screaming "FEED ME!" My opinion is to repot into some fresh cactus soil, dont water for a week at least, and then give it some fertilizer once a month at half the rate. Mammillaria do not require full sun, and will do well in partial shade.

I was thinking over watering during the winter. You can easily do that with these guys, although since you have had it for 20 tears I doubt that's the case.

I feel I should clarify a little.

While they will do well in partial shade, I grow mine in a sunny spot outside where they get strong sunlight avoiding only the hottest midday sun. I almost never water during the winter, with just a taste to keep the roots from drying out completely. They do not need to be misted, just soak the soil once once a month from March -June, and then twice a month through September if it's particularly hot and dry. If yours is inside, once a month will be fine, and maybe stop all water after Labor Day except Thanksgiving and Super Bowl Sunday. Then start again once a month in March.

Good luck!

Thanks for the help everyone. I went to investigate the soil a little around the base of the plant and realized there is a bit of rot going on as well.

I think I'm going to do some surgery on him and try to get a few cuttings from the still healthy stalks and start myself a new plant.

I sure hope I can get at least a few cuttings to root--I've had the plant for so long I want to keep him in at least some version.

This rarely happens with me as I am known for my neglect when it comes to watering, but this winter, I had a Dog Tail Cactus in my cool greenhouse and it got cold damp "feet" and the tips began to turn brown eventually traveling back towards the center of the plant. I took the plant inside the warmth of the house, cut away the rot, and placed the plant in good light just above the baseboard heat to warm, and dry out the soil a bit. It now it is doing well with new growth, and I am very happy that I caught it in time. I'm sure you will be able to save your beloved plant, but taking cuttings as insurance is a good idea. Hope all works out well.