I'm not sure what you mean by 'physically reroute traces'. If you mean, physically move a metal trace across the chip, that's not really possible at this point.

One-time programmable devices (GAL and PAL devices that are essentially obsolete, most FPGAs are SRAM based these days) require physical fuses to be blown in order to program functionality. I suppose that's a physical change, but one that's irreversible.