“Nursing homes are legally permitted to evict residents under several conditions: if a resident’s health improves sufficiently; if his presence in a facility puts others in danger; if the resident’s needs cannot be met by the facility; if he stops paying and has not applied for Medicare or Medicaid; or if the facility closes. Facilities are obligated under federal law to give 30 days’ notice, in writing, and also to work with the resident on a transition plan.”