I don't think the club losing money affects SD in the slightest, the only way it'll hurt his own pocket is if he subsidises losses, but there's no onus on him to actually do that. The club has its own income and expenditure, with the assets and loans all secured against one another. If it ever came to the club going bust, it wouldn't hurt him whatsoever (other than obviously losing whatever money he paid for the club and denting his pride). I don't buy that financially he's struggling - he's selling because he wanted to flip the club for a profit and has realised he can't get the club back to the Championship to do that. His balancing act is working out how long the club can stay afloat without denting his asking price. The sale of academy players, redundancies and long term furlough is all done with the intention of maximising the budget and keeping the club running with that in mind.
I think it does like. Where else, apart from the owner/shareholders can the club get funds from? A loan? Already got a £10 mil one secured against the assets. Overdraft? Can't see that stretching to much. As for going bust, not happening. Don would lose all the money he's put in and his business reputation would take a massive hit as being the person who bought Sunderland at their lowest ebb and managed to take us even lower. Selling at a loss may be a bit of a cash and ego hit that he doesn't want to take but I think the alternatives are worse.