Possibly require that the former owner be required to handle all of his units maintenance for the reduction in market rent during his stay. 

While it would be a bitter pill to swallow if things somehow went sideways and we had to pay, we definitely would to protect our credit and because it’s the right thing to do; thankfully we’re Blessed to be in a financial position that we could do that.

He's asking for a $300 reduction which is $3,600 in lost income for one year. 

Now with the rental market in flux, the remaining one is asking for a rent reduction, though not because they lost income due to Covid, but because it's not easy to find a new housemate. 

Whenever you live in an inflationary environment, asset-focused fixed debt is incredibly valuable for building wealth and hedging against the reduction in purchasing power.

At some point the tenant might ask for a rent reduction or even to threaten to take the item they installed if the relationship sours when they move out.

Once you make a reduction for one thing, the tenant will find other reasons for other reductions or may want more of a reduction than you're thinking of offering. 

I wouldn't say that you are necessarily obligated to reduct the rent, but it's something that would be appreciated.

As @Steve Babiakmentioned, you aren't likely to be able to negotiate for a reduction in the amount of back property taxes owed.

Markets have cratered before.. in 1989 to 1992 for instance prices in the SF bay area dropped 10 to 50% across the board.. even SF saw price reductions of 50%...