Yes, you can buy it. It's very common at wholesale banking levels (credit default swaps are extremely commonly used to cover counterparty risk). Also credit insurance is available to anyone.
However, the simple option here is to put money into short term govt bonds, there are ETFs like SGOV that make this extremely easy.
Even more ridiculous is that you are getting 4-5% yield on them.
This is what is so crazy about this entire saga - people should not be parking millions upon millions at a bank earning no interest when you could be getting 4-5%+ - regardless of solvency issues.
It is frightening to me people don't seem to understand this. It's absolutely basic money management. It would be more understandable when interest rates were basically 0 and you wouldn't get any yields from bonds. But that isn't the case and hasn't been the case for a long time now.
Now clearly SVB were offering perks for doing this, but say you had $100m parked there, are those perks really worth $5m/year? People should have been asking that. It's a whole team of engineers paid for!
And really offering personal perks to founders contingent on company money doesn't sit completely right with me, unless the founder owns 100% of the equity which most do not. It's one thing offering perks as goodwill but putting convents etc on company money for personal perks is suspect to me.