It doesn't look any different from a return for someone who is 25 years old and moved out of state in January 2025 for a job that pays twice as much.  Don't overthink it.  However, if the niece lives in California, consider filing a nonresident return showing zero California income, since the FTB can be vicious about pursuing anyone with a California address.  I've had that happen with a California daughter using her address to file a return for her mother, an Arizona resident.  Same situation may apply to New York.  

Or, ask the nursing home if they can accept and forward mail for patients.  Without charging too much for the service.  And what mail are you expecting anyway, if you have the refund deposited directly?  Alternative, file with the nursing home address and then follow up with an 8822 to IRS.