Why couldn't you enforce the lease if the tenant has to move into a care home? Is that a State law where you are? We put a clause in our lease that says the lease must be fulfilled no matter what happens in the life situation of the person renting. There is a buy out fee (usually equal to about 2 months rent) if the tenant needs to get out of the lease early. We also allow them to transfer to another unit we manage (for a fee equal to 1 month rent.)
I do understand that enforcing the lease does not mean collecting the money owed to you so that's always a problem.
That being siad we often do MTM leases after the first year but we always charge about $75/month more than the year lease price for that privilege. A lot of people are willing to pay that amount if they don't know what is going to happen in their future or they need a few more months before they move.
Lastly, if it took you 5 months to rent your property there are probably some things you can fix in your leasing strategy. Even in winter 5 months is a long time to rent a property. Looking on how you can sure up that part of your business can give you more confidence in situations like this.