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Yes in certain situations a tax deduction could still be claimed if the original asset is gone, but the loan used to purchase it is still going. Best to get advice well before selling for this.

The bank will not discharge the mortgage until their loan is repaid. So you will need to come up with the full amount of the loan in order to settle - ie pay the bank another $40k at settlement, based on your example. LMI will only help the bank if you default and cannot pay. It won't help you.