Usually the central bank deciding to go negative try to not really explain the borrowing part (because it's really bad press), but they DO give free money to banks that borrow from the central bank. Like
@neroden said, it is a prop-up program for banks.
This NYT
Sweden Imposes Negative Interest Rate and Plans Bond-Buying Program articles explains:
"The decision means that Swedish commercial banks will be able to take out loans from the central bank at a negative interest rate. When the loans are due, banks will pay back less than they borrowed."
It's true that the Fed has never gone negative and hopefully they never do. But if they do, you can be assured they will create new money and give it away, never to be returned, to at least the member banks. It's possible that all banks would have access to free money as well, but its hard to imagine that foreign banks would be eligible. The hoi polloi won't like it either way.