Revenue wants to be paid within a year from when the person passes, if this is done no interest is due. If it is not paid within the year interest is charged from the date of death until payment date, so no free year. I think the revenue interest rate is a hefty 8% annually.
We left a house empty for a few years when its owner was in a nursing home under F/D for the same reason, fear of the tenant overholding when the time came to sell, and / or a troublesome tenant. It can take a long time to get a tenant out if they don’t want to go. Also no one wanted to take on the jobs that go with renting;
Sourcing and vetting tenants, dealing with the PRTB
Dealing with maintenance issues etc.
Doing tax returns.
Dealing with tenants if they don’t pay or overhold the property.
If your brothers have POA, is selling the house an option ? If so you can now sell and the house sale proceeds will not be assessed when calculating your mothers monthly payment.