When Norway went into lockdown, they predicted a similar problem. We have decent unemployment safety nets here, but the process takes a bit of time and the fear was that the bureaucrats would not be able to process the applications fast enough.
However they rose to the occasion and managed to come up with an online-based solution in 3 days. There's an interesting write-up here[1] (in Norwegian, but Google Translate should do a decent enough job).
A key point was that the legal department managed to find some wiggle room in the rules to allow them to pay out in advance of the application getting officially approved. However there was also some legacy systems to contend with, and of course the web site had to be secure since it had to process our equivalent of social security numbers etc.
The result was that in a few days they processed more applications than they typically do during a normal year, and people got their money.
[1]: https://www.kode24.no/kodenytt/slik-koda-nav-ny-dagpenge-los...
And how many of those people won't go to a hospital because they're uninsured now?
Some laid off have benefits for longer.
There are definitely some people in low wage states getting more but that is far from universal even though it’s a standard right-wing talking point.
If you are furloughed you keep all your benefits and still qualify for unemployment
Some companies are paying for healthcare for a period of time post layoffs
The reason why a lot of people can’t pay is not because they won’t have that money eventually but because the state unemployment benefit offices are steeped in bureaucracy and aren’t processing these claims fast enough. Some states make it much harder than others by design. This is a preventable crisis.