I don't know about the borrowing system, but I believe there are several Lisps that avoid mark-sweep garbage collection. NewLisp is one such example, though I think they sidestep the issue by copying everything by default and using efficient allocation/deallocation.

Memory safety is compile-time guaranteed except in unsafe blocks.

It's a little less strong than your impression. Memory absolutely can be a problem, but instead of looking over the entire program to find it, you know the problem comes from a marked unsafe block.