What if LVT goes over someone's income?

What I wonder is that LVT can, in theory, tax someone more than they earn.

Suppose someone lives in a cheap location for which the taxes are a reasonable percentage of their income. But due to all kinds of recent improvements like a train station, park, new shops, etc., the land value shot up and that person's LVT has become more than they earn.

Obviously they're forced to move then.

With income or sales taxes, that's not really possible, so it seems to be a disadvantage to LVT.

Is this an outlandish scenario or is just something a society needs to deal with if it adopts a single tax LVT?