I think you've gotten good advice so far. I do not believe from my landlording experience that you will be in any trouble by saying "Hey I'd like to rent to you, but this is a time when folks can park themselves in someone's rental and stay there rent-free if they lose their job or lied about it or whatever. Just like credit reports track a person's history, spending, activity, and track record, I am not willing to rent to someone who has no landlord references to check, etc." On the other hand, I would agree with where Karl is headed, and that is that there may be some legit extenuating circumstance that has led to this unique position. And remember, if a tenant is asking you to bet on them and pay as they go, it's one thing, but in the case of some folks with a serious disruption to their life, they might have the money to pay for 1st, last, security, and hell - second to last - and that would probably reduce your risk.
It's a weird time, lots of things are happening to lots of people, the govt. is preventing evictions, and you're in the business of providing housing. On top of the usual issues with "tenants, trash, and toilets." Not an enviable position, by and large :) Move to passive investing in apartments and industrial and self-storage and data centers as soon as practically possible.