If inflation truly starts to rise, the Fed has indicated over and over that it will raise rates in response. Mortgage rates will ultimately rise, making housing less affordable (on a monthly basis), thereby forcing housing prices down severely. So the current mortgagee may have an easier time with his mortgage payment, but he won’t be able to refinance, and worse yet, the mortgage cost might vastly exceed the value of the depreciating house. I don’t see runaway inflation as a threat at this time, though.
That said, the uptick in the yield of the 10-year should be of great concern to homeowners, as that will also push up mortgage rates (which are, in fact, currently rising.) That’s bad news for an already beleaguered housing market.