If the bank wanted to let you bring the account current, they certainly could have done so. But, they didn't. Now, the car is sold and gone - there is nothing to reinstate. So, you owe the deficiency.
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I would suggest that you read the loan contract you signed for information about the right to reinstate. In many states, this right is only available by contract. In other words, if it isn't provided in the contract, it is a discretionary decision for the lender to make.
It is probably too late to do anything now, unless the contract gave you specific rights on on the off chance that state law incorporated this right, in which case, I would suggest seeking legal representation.
Hope this perspective helps!
If the vehicle had not yet been sold you might have been able to recover it by filing a Chapter 13 bankruptcy and catching up on the arrearage in your payment plan. As that is not an option, you may be able to defend the $10,000 remaining balance if the creditor sold your car off in a commercially unreasonable manner, i.e. a $22,000 car selling for $12,000 sounds a little off. If they sold the car in a way that is unreasonable, you may be able to recover damages from them or negotiate a much smaller settlement.