Mrs. Rose is a hospice patient in the nursing home. She has gangrene of her foot. What can she do to cure it?

It depends. Depending on her current health status, whether the gangrene is wet/dry, if there is neuropathy (which may spare the patient pain), and prognosis are to all be considered. Hospice care is palliative in nature, so if intervention for the gangrene is to be considered, a change in her hospice status is necessary.
Contradictory. Hospice patients are usually at the end of their life and the hospice care is to relieve pain and permit a dignified death. Gangrene usually requires amputation or debridement of all dead and/or infected tissue. Mrs. Rose would need to be taken off hospice and transferred to an acute care hospital for podiatry and infectious disease and/or vascular surgery evaluations.