Medicare will pay for 100 days of nursing home care after a qualified event and it must meet a very strict set of qualifications.

First: The first hurdle is you must enter the nursing home with-in 30 days of a hospital stay covered by medicare that lasted 3 full days or more.
Second: You must get a note from the doctor and it has to be for the same reason you had the hospital stay.
Third: It must be an Acute condition, one that is believed to be cured in the near future.

Dressing, bathings and those types of things are typically under custodial care which are not typical a direct reason for medicare to pay.

Ideas: You can work with local and state organizations who may provide this type of benefit at the state level. In Texas my father received it because he was a veteran.

Medicaid may also be an option.

Long term care insurance will probably pay for it, if your family member purchased it in advance.

Depending on the plan your Medigap plan may provide coordinated benefits in conjunction with approved medicare expenses based on the policy specifications.