Can he buy a car from an auction held by the riba-based bank, on which the owner defaulted on payment of what he owed?

Praise be to Allah.

It is permissible to buy a car from the auction held by the riba-based bank, subject to two conditions:

1.. That the owner of the car has given permission to the bank to sell it, or the court has issued a ruling to that effect, because it is not permissible for the bank to sell the car that is being held as collateral without the permission of the customer, unless the court has issued a ruling to allow that.

It says in Zaad al-Mustaqni‘: When the time for paying off the loan comes and the borrower refuses to pay it, if the borrower gives permission to the lender to sell it (what is being held as collateral), he may sell it and pay off the debt, otherwise the judge  may force him to pay off the debt or sell that item that is held as collateral, and if he does not do that, then the judge may order it to be sold so that his debt may be paid off. End quote.

2.. That the car is offered for sale in the auction at the market price, similar to the price for which other used cars like it are sold, because it is being sold on behalf of its owner to pay off his debt. So it is not permissible to sell it for less than it is worth, or to take any of his wealth without his consent.

It says in Mughni al-Muhtaaj (3/71): The man of fair character should not sell an item that is being held as collateral except for the market price, to be paid immediately in the local currency, and he is to act like a wakeel. If he does not fulfil one of the conditions of acting as a wakeel, then the transaction is not valid, but it does not matter if the item is sold for a little less than the market price, which is a common practice among people, because they usually overlook such a small amount. End quote.

The man of fair character is the one with whom the collateral is kept, if both parties agreed to give this collateral to someone to keep it.

If both conditions are met, then there is nothing wrong with buying it.

There is also nothing wrong with buying from this one who was forced to sell.

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said regarding one who is forced to sell in order to pay off what he owes:

Is there anything wrong with buying from him? The fuqaha’ (may Allah have mercy on them) say: Buying from him is disliked (makrooh) because he is selling under compulsion. The Prophet (blessings and peace of Allah be upon him) forbade buying from one who is forced to sell, and this man is being forced to sell. But the correct view is that there is nothing wrong with it, because if we say that it is disliked (makrooh), that would only increase his suffering,  and if we tell the people: Do not buy from him, when the lenders are hitting him morning and evening and demanding that he pay them fifty uqiyahs of silver (for example), then he will be constantly suffering from compulsion. So the correct view is that there is nothing wrong with buying from him. In fact if it was said that it is recommended (mustahabb) to buy from him, so as to relieve him of this suffering, that would be a good reason. As for the hadith mentioned above, it should be understood in the opposite way, that is, when a man urgently needs something that you have, then you should give it to him at the market price (and not increase the price, thus taking advantage of him)." (Ash-Sharh al-Mumti‘ (15/488).

See also the answer to question no. 146305 .

And Allah knows best.