Property taxes incurred prior to the date of filing bankruptcy are disallowed to the extent that they exceed the value of the property to the bankruptcy estate (Bankr. Code Sec. 502(b)(3)).
Property taxes incurred after the date of filing are not discharged, so you owe on them. However, as a practical matter, if you walk away from the house, then the lender will have to pay the property tax bill, or it will lose the property to the State. This would discharge your obligation to the State, but the lender could then attempt to collect against you for its having paid your tax bill after bankruptcy.
Whether or not the lender will actual sue you is unknown. It's entirely up to the lender's discretion about whether it wants to spend the money to try to collect.
Hope this helps.
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