Seriously?
There is NOTHING unreasonable about a landlord wanting the rent to be paid. That is, after all, the whole point of renting - exchanging a fixed amount of money in exchange for living in a sound building.
If the tenant could not afford $1300/month in rent but signed such a lease anyway that is NOT the fault of the landlord - that is the fault of the tenant for making a poor financial decision.
When a tenant has a financial upset the ethical thing to do is go to the landlord and explain what the situation is - which it sounds like happened in the OP’s scenario. Now, the landlord is under zero obligation to renegotiate or change any terms. Many will do so, because losing a tenant case be a hassle, and evicting one is always a hassle. But no landlord has to do that. It is entirely legal for a landlord to begin eviction proceedings the first time rent is missed (although right now evictions will be on hold in some places, but that won’t last forever).
The OP generously cut the tenant some slack. But there is nothing unreasonable in wanting the rent money because a landlord has bills, too. A rental property isn’t a charity, and even when it’s run as a non-profit there are still bills to pay, taxes, maintenance, etc. Now the landlord knows the tenant has received some money it’s not at all unreasonable for the landlord to ask the tenant “hey, will you pay some of that money you owe me?”. I don’t think the landlord is expecting the tenant and kid(s) to go without food, but speaking as a tenant, I’d personally would at least offer $50 or $100 towards any rent owed as a gesture of good faith even if I can’t pay it in full. Because the last thing a landlord wants to do is have to chase you down.
Other things I have done when strapped for cash is offer to mow the lawn, tend the landscaping, do simple repairs, etc. The landlord won’t always take a tenant up on that offer, but some will.
This is going to be a problem for awhile, because a lot of people have lost income but their name is still on a lease.