Hold or fold?

[Account Closed]

An older friend (close to 70) owns a rental that makes a small positive cash flow.
There is an existing mortgage of about $15K which he could pay, but has been saving that $15K (and more) for down payment when he finds another house to buy--which would also be a rental. He had been hoping to buy after prices fall even more. (2 rentals plus his home)
With the economy being what it is, he is concerned about banks failing and losing half or more of his money to runs on the banks, a recession/depression, and possibly losing that house unless it IS paid off, so is thinking of paying the mortgage off. Then he wouldn't have enough money for a downpayment on almost anything. Paying the mortgage would increase the cash flow of course, but not enough the spent money could be replaced anytime soon.

His personal income is enough to live frugally since he owns his house. No, he's not interested in or able to sell either place right now.
What advice would you give him? Pay the mortgage off, keep the full amount and wait for prices to come down, what?