For you or others, hospice doesn't have to be moving to a hospice facility. They will come to wherever the patient is at. For my mom, the main point was that she didn't want to keep going to the hospital for care. I told her it was her decision to switch to hospice and that we would also end up whenever she wanted.
Now if you have hospice care at home, obviously the care isn't as on-demand as it would be in a facility.
EDIT: Hospice is also there for the family of the patient. When my mom passed at the assisted living place, hospice was first informed and then reached out to me. They took care of the initial details such as reaching out to the funeral home, that was previously identified, to get the process started. While I could have done all of that, it was nice to have someone else handle it. They also offered grief counseling to the family, not that I'm aware if anyone took them up on it. Once again, all free to the patient and family outside of medicare premiums.