If it turns out in our company that someone is going to be out an extended period of time there's other options like FMLA, Short and Long Term Disability, but I've found the unlimited PTO perk at our company with several individuals a real thing.
I've never been denied a request. I don't abuse it either, but I've never been denied a request or been told..."Sorry you've already taken this many days."
Now I can only speak for my department, it might be different elsewhere in the company. We also don't have to build any up or accrue it either. You just take it when you need it.