We usually think of wages as payment for work produced, and generally, if the cost of producing a thing isn't exceeded by the value created, you won't pay that cost.
But the true cost of labour is its upkeep, sustenance, that of its family, the training, risk, and uncertainty associated with the employment, as detailed 245 years ago by Adam Smith (Book 1, Chapter X, Wealth of Nations).
And that means, in a time when work is impossible, paying a maintenance wage to ensure future productive capacity.
But virtually no states offer unemployment insurance as a routine basis for self-employed individuals, which would include individuals with small businesses, gig workers, or independent contractors, which largely describes housecleaning services workers.
The US did pass emergency national legislation (the CARES Act) which allows (but does not AFAIU require) states to extend unemployment insurance to those workers. See: https://web.archive.org/web/20200617001228/https://money.usn...
Mind: I agree with your point from an ought perspective, unfortunately the is is at odds here. For the US, this means individuals have to step in.
My comment above only means to illustrate the economic rationale by which one might choose to do so. Unfortunately given market mechanics, most people will like decide not to. That's the cause of much of the economic disruption and dislocation of the past year, in the US and elsewhere.
Cons: Totally arbitrary. Have a generous employer? Great! Stingy employer? Sucks for you. I'd also imagine that whether you'd get this kind of "relief" depends on your job, kind of like how waiters get tipped but fast food workers don't.