The logic is as follows:

This is a liquidity problem (so far). This isn’t because loans went bad or anything, just that they needed cash quick and had to fire sale things (the things they took losses on were US Treasuries. Mostly.)

They still have a big loan book that is probably worth more than their liabilities.

A large player with liquidity could get those loan assets on the cheap if they agree to provide the short term capital liquidity (a reassuring name also probably stems any bank run risk).

Also the FDIC is pay in pay out insurance. The commercial accounts at SVB are in the hundreds of millions and no payments were made for those accounts. The FDIC probably won’t help.