They have that problem, but there are frequently programs or legislation designed to reduce that burden. Eg, >10% of Americans are (theoretically) covered by Prop 13. Other municipalities may have laws on the books limiting property tax increases to a certain percent per year. Many other places offer property tax relief programs for people with low income, or the disabled, or the elderly, or generally by increasing exemptions.

As I understand it though, you wouldn't want these programs with a LVT system, because they would just distort the market in a similar manner that it is now?

Yes, because of the property appreciation, Terry can say that on paper, he is rich-ish, but a weird kind of rich where he has nothing but a house in a nice neighborhood, and otherwise has very little money.

How does he pay off the taxes with the equity of his home? A HELOC could work, but he already can't afford the increased taxes with his income alone, so a HELOC would just delay the inevitable and based on his income he probably wouldn't qualify for one.

Or he could do a reverse mortgage, be able to pay the taxes, but put himself at a major risk of losing his home entirely if he lives long enough. Also, reverse mortgages are only available to people over 62.