The transition from "short-term rehab" to hospice is not unusual. For a variety of reasons, your family member may go to short-term (or "subacute") rehabilitation, expecting to get better and go home. Unfortunately, this doesn't always happen. Your family member may not be strong enough to fully benefit from rehabilitation, or illnesses may have progressed. Sometimes, the doctors in the hospital cannot tell if a patient's health is going to improve or get worse until rehab is tried. Talk with the doctor at the rehab and make sure you have a good understanding of your family member's diagnoses and prognoses (the expected course of your family member's illnesses).
Hospice isn't for everyone. It's a choice, not a requirement. The Guide to Hospice and Palliative Care can help you understand what hospice could mean for your family member, and what it could mean for you. This guide can also be a good tool for the entire family to use when talking about hospice - this way everyone has the same information and can make an informed decision.