Do I need to file for guardianship for older disabled sister with stroke?

My older sister, who is disabled ,on social security and lives alone, just suffered multiple strokes. She is paralyzed and cannot speak and is on feeding tube. Hospital wants to discharge her immediately to nursing home. She has no assets-lives month to month on SSI. I'm the only relative and the hospital wants me to file for guardianship and then Medicaid to place her in facility. Do I need to do this- why not just let the state handle it? (She has no home, no savings, except monthly social security which she spends in full). She has left no directives and I dont have POA.