If you’re old and no longer have much of an income, you still have your home. If you become disabled,

We already have this is many states in the USA. Its called the "Homestead Exemption". Here's an example from Ohio:

"This is a statewide program, administered by County Auditors under rules established by the Ohio Legislature and the Ohio Department of Taxation. This allows senior citizens (65 or older) as well as permanently and totally disabled homeowners to reduce their real estate taxes by the amount equal to the taxes that would otherwise be charged on $25,000 of the market value of an eligible taxpayer’s homestead or residence. The homestead may include up to one acre of land. Under the changes made by the Ohio Legislature and beginning with applications for tax year 2014, new participants in the program will be subject to an income test to be eligible."

So matter how big your house is (as long as its on one acre of land or less and you have an income $$75k/year or below) you only get charged as though the house is worth $25k, which I think would obviously be a very low tax bill.