I don't have any experience with hospice yet, so I'm trying to figure out what kind of hospice care these coworkers are providing at work. Are they managing his medications? Applying topical lotions? Changing colostomy bags or wound dressings? Providing talk therapy? Responding to seizures?

Or is LW using "hospice care" to mean "this dying coworker is here at work while dying, and while we're not providing medical care, we are uncomfortable having someone in our midst who's going to be dead in a few weeks or months"?

I've absolutely known people who loved their work enough that they'd have wanted to keep working for as long as they were physically capable of doing their job. I've also known people who'd stay because they felt they had to, or because they couldn't afford to quit and lose insurance.