It would most like be battery cables, corroded or loose.
And negative cable is a power cable, because there is no positive unless there is a negative :)
Yes, there will be fusible links for the alternator's B+ wires, at the starter relay end.
And Fuses #4 (40amp) and #12 (15amp) in engine fuse box.
But these are for alternator only, so wouldn't effect lights as they would continue to be on with battery power after engine/alternator were off.
But engine stalling would indicate power to computer or ignition was cut.
There are a few fuses in engine fuse box that can blow and cut power to several systems, #2, #4 and #10 (60amp)