If someone lost their house to the bank, the bank would be liable while they control the house. Main focus is on empty rental units or empty investment properties.
Presumably you'd need some window of exemption for normal transfers and typical moving times.
I'd probably implement as ~2x property tax on dwellings unoccupied for more than 3 months in the past calendar year. As you pointed out, this would have a downward pressure on rents, as landlords would be less able to leave an apartment empty while they wait for someone willing to pay the highest rate. Also, people who own multiple houses would be penalized for keeping some of those houses empty without renting them out.
Presumably you'd need some window of exemption for normal transfers and typical moving times.
I'd probably implement as ~2x property tax on dwellings unoccupied for more than 3 months in the past calendar year. As you pointed out, this would have a downward pressure on rents, as landlords would be less able to leave an apartment empty while they wait for someone willing to pay the highest rate. Also, people who own multiple houses would be penalized for keeping some of those houses empty without renting them out.