It issues an IOU for sats similar to the state banks in the US in the 1800s.  You deposit some gold (sats) in the Bank of Kentucky (cashu mint) and you have a promise to redeem that IOU for the same amount of gold at a later time.  The bank assumes the risk of storage.  

If the bank (cashu mint) remains solvent and in business (two different things: think of the guy in the front of the line in a bank run and the guy at the end of the line) then the “bank note” (cashu token) you received held its value.

Then instead of just keeping the IOUs they started to use them as currency, where other businesses would accept notes instead of just gold.

This is the step that makes cashu win.  It’s not a savings tool, that’s Bitcoin.  It’s a bearer asset with several use cases.  Privacy and fungibility among the strong points.

And regarding your last paragraph, you don’t hope to get “some” of your value back, you hope to get all your value back.  Proof of liabilities and proof of reserves are in work and there will be risk, but I think the future would be better if professionals ran lightning nodes (I hate to use the term “banks” here, but call them Cashu mint operators) and we all zapped around Cashu tokens with no ( or very small ) fees.