If the lender sells the property at a loss and you owed them a sum of money owing under the mortgage then they may seek to get judgement on that debt in the UK.
They would first have to issue a claim at Court and get judgement on it, which is not practically difficult. They would also seek to include their legal fees for this in judgement debt.
Once they have obtained judgement in the UK they can then seek to enforce this against you. Usually this involves registering a charging order against the title of your property. They would have to apply for a charging order, registered first as an interim charging order, a hearing will be set for whether a final charging order should be registered.
Once the final charging order is registered against your title it would prevent the sale of the property without the lender's consent, which in reality means that they shall not consent to the sale unless the money is repaid upon completion. They could apply for an order for sale of the property. You would be informed of any such application and would obviously make representations as to why the order should not be made. These orders are considered only as a ultimate sanction by the Court and they have very wide discretion to to consider your welfare and housing requirements and those of your children (if any) and a number of factors are considered (size of debt, repayment suggestions, whether the debt will actually be repaid from the proceeds of sale, the fact that is his and your home).
Sorry it could not be better news, it's a very difficult situation and you have my sympathies.
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