In California that's called Proposition 13. It's not quite an exemption per se, but property taxes do not spiral out of control as home prices do. My next door neighbors in their mid 80s, who are original owners of their property, pay about $2800/year in prop tax on their house. They'd have been absolutely forced out long ago if they had to pay based on current market value of their house. Progressives want to remove that protection.