Was VMWare dying prior to the acquisition? I don't really know the financials but that wasn't the impression I had.
Dying no, but their business certainly had a downward trend on it since so much is moving to containers instead.
VMWare din't have a growth trajectory and didn't have a reasonable expectation of one.
You don't make these kinds of sales when you're circling the drain, you do it when you can see that future coming for you.
No, but Broadcom didn't buy them to build a company over time. They have a long pattern of buying a tech company, jacking up the prices, and making enough money (before customers switch) to more than make up for the purchase price of the company, netting them a tidy profit. Plus, at the end what they're left with isn't completely value-less either.
Everyone who followed Broadcom (and that included many VMWare employees) knew exactly what was coming the moment the acquisition was announced.