GMAC, now called Ally Financial, was just about to receive the last of $17 billion in taxpayer bailouts. The board, including directors named by the government, discussed whether to use bankruptcy to get rid of toxic mortgage assets that were pulling down the rest of the company, according to people who attended the meeting.

Alvaro de Molina, GMAC’s CEO at the time, disagreed. The move, he said, would lead to years of fights with creditors and tough treatment from regulators that …