I'm surprised financial services have not popped up just to help people in such situations. The service could confirm the person has as much coming as they say, have him sign his life away to them, and then float him enough cash to buy the stock and pay the taxes on time. Then the employee pay some portion of his new wealth to the financial services company.
They do exist but are very expensive. Basically by the time you go to them they know you are screwed and in desperate IRS-caused need of liquidity. So while the actual estate tax may be 40%, you wind up paying 50% or more. This is usually a debt deal, not an equity one - who wants shares in a closely held family corporation?
For developers at unicorns I think services are somewhat better (e.g. secondmarket, elite crowdfunder).
Does that really not exist?