If I value my property at a dollar, I'm signalling that I don't want to pay property tax and don't have the slightest interest in selling my property either, ergo there is no reason whatsoever for any speculator to waste their time bidding on it (unless the government becomes a property speculator, or somebody with deep pockets really resents my tax avoidance).

Of course, the system also needs a mechanism to deal with the opposite: nuisance bids from people who don't have the will or ability to actually complete the purchase. Buying property is not like buying shares.