That solution would be a second form of price control. The eviction ban is the first one. The primary problem facing renters is wage stagnation, wealth depletions and inflation. What needs to happen is for rents to fall. That would have happened if they never put in an eviction ban, in the first place, and allowed the market a month or two to balance itself out.
Instead, we have the worst of both worlds. Higher rents and renters with less money (unless they've saved it while not paying--another problem).
In short, the big question isn't the old rent, it's paying the new rent. The good news is Mr. Market has an answer to the pandemic's price controls. After August 1st it will most certainly be in the mail.