Sure, your taxes can increase. I'm talking about the bank asking you to pay down a part of your principal. Because the value went down 10%-20%.
No, I don't think that is standard anywhere, and I believe that it would be historically anomalous for a mortgage. (Revaluation in real estate I believe is normally only associated with leases; while there are some oddball mortgage situations -- for instance, I think in Hawaii that leasehold mortgages actually do exist -- I don't think revaluation even comes into play with those.)
So the question that came to my mind was how do the MBS folks and GSEs handle this? I knew that that prepayment is treated as an option, and it turns out that appreciation/depreciation/default/odd-loan-to-value can also be treated as a default option -- and that the Federal Reserve and the GSEs have had folks looking at that very subject. Here's a recent Fed paper on the subject (I first found and read an earlier version, but I have only skimmed this final version which looks much better than the one that I read): An Empirical Test of a Two-Factor Mortgage Valuation Model: How Much Do House Prices Matter?