In some other countries, including here in the UK, the blow of the pandemic to employment has been reduced, or at least delayed, by government support for those who are unable to work.  In the UK the government pays 80% of wages for anyone who is unable to work due to the pandemic through the Job Retention Scheme (the furlough scheme).  Similar systems have been set up in Germany and France.

The biggest cause of fraud is the fact that the US government has a difficult decision to make.  As unemployment rose to around 15% in the US in April compared to less than 5% in the UK, there became a very difficult balance, as underfunded services for dishing out unemployment benefits were overwhelmed, between having appropriate security measures in place and being able to give the people who need it most their money.  There's also the problem that the poorest people in society may find it the most difficult to prove that they deserve unemployment benefit.  Because there's no support for people in work to prevent them losing their jobs apart from the small 'stimulus cheques', the US system is a kind of 'whack-a-mole' approach that leaves it open to all kinds of fraud.

There is some fraud in the furlough schemes, but as far as I know it's not on this kind of grand scale and people have generally kept their jobs so far.
I think the best thing governments can do is prosecute people who are believed to be engaging in this kind of fraud.  That means opening up courts properly - I think that restrictions on courts opening fully and trials with juries do more harm than good.  Blockchain may not have much of a role to play because the problem is not verifying where the funds go, it is determining whether they were obtained fraudulently.