If you've defaulted on your mortgage, the lender would be entitled to charge you with the amount of the unpaid loan, late fees, and their expenses in foreclosing, which would include the back property taxes and foreclosure fees.
However, in CA, borrowers are protected from deficiency judgments (the difference between what you owe and what the house sells for at foreclosure) if you have a "purchase money" mortgage, meaning money you borrowed to buy the house, and not a home equity loan, and not a refinanced loan. The bank is the one that takes the risk that the property will be foreclosed, and they can't go after you for the loss they realize when the market turns down and borrowers default.
Banks deny short sales for many reasons, and sometimes they are just too disorganized with the loans being re-sold so many times that they can't get the loan's owner to approve a short sale, or they have short term time frames and don't want foreclosed property on their books so they might approve a short sale. If they don't mind holding onto real estate until themarket recovers, they might be more inclined to foreclose and keep the property.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
You are responsible for back and current property taxes so long as you own the property. The bank may include such taxes if included as part of foreclosure. The bank may be denying a short sale in order to foreclose.
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