Assuming that these people have a line of credit available and didn't use it all up buying boats, RVs, and doing a fancy kitchen renovation, they could use that to pay off their balance and sell their vehicle privately, then put all that money on their line of credit. But five digit private sales scare me. My CBR125R is the most expensive thing I've sold privately and was nowhere near five digits.
Another option is home equity loan, assuming they have more than 20% + what they need to borrow equity on their home.
People do put themselves in a pickle doing zero money down this, 5% downpayment that, max out all their credit, etc.