Can negative cable from a car get so hot it cut off the car?

You mean; it actually melts loose from the connection?

I don't see why not. A badly frayed cable will not have enough copper strands in it to carry the proper current, especially when on a heavy load like starting or, say, if an alternator diode shorts. A very poor connection at a terminal can also get hot enough to melt. A good battery can supply hundreds of amps in a short time, like a spot welder. A shorted started can actually get welded together by a good battery.