Brex could offer loans up to 25% of the borrower's funds stuck in SVB. As long as depositors receive at least 25 cents on the dollar, the loans would be paid back in full, and the borrower would have gotten significant working capital in the interim.

SVB's carcass still has significant assets, so Brex can set that % number based on what they know about SVB's state, to make the loans almost risk-free.

I'm not a banker and have no idea if this is actually what Brex is offering. That public page doesn't discuss terms at all, which makes sense given the chaos. But there's certainly ways to structure these loans without much risk.