The AOAO first puts a lien on the property. That lien puts a cloud or hold on the title, so it must be paid before you get clear title. Also, the mortgage company is not going to let the home go for $1. They probably won't send it to auction at all. In most cases, in Hawaii, they will get an agent to market it, and sell it "As Is."
The mortgage lender has to release their interest in the property (the $300K in your example), and sell it for market value. That is defined by whatever someone will pay for it (and they will accept). It could be $200K or $300K. The mortgage company must pay the association dues (starting from when they took title), or they can't pass clear title.
The AOAO may also foreclose on the mortgage company (for not paying AOAO fees), after it has foreclosed on the homeowner. The AOAO may also seek a judgment on the original homeowner for any gap between what they owed when the bankruptcy or foreclosure occurerd and they fell behind on payments.
Call me if you have further questions. I am the treasurer at my AOAO and have foreclose on two units for non-payment.