In a normal ebike setup there are a number of overcurrent protections that I can think of..
The battery BMS FETs should trip a little over the batteries nominal max current rating.
The battery normally has a back up fuse of higher rating over that again.
The controller normally has a shunt that measures the battery current and should (hopefully) limit/shut down/error in event of motor short.
Low wattage carbon resistors are used internally that will fuse if external shorts on 5 volt, headlight circuit etc
PCB tracks, are often intentionally very light copper with solder (low melting point) that will melt.
Battery balance wires etc are very small gauge and will melt.
External 5 v line normally via diode
Many components will 'blow' open circuit.
Good quality chargers normally have additional built in protections as well as the standard fuse.
A big problem I think can be when attempts are made to modify/repair by upgrading components . (e.g fuses or fitting thicker (e.g balance) wires in battery etc or replacing a carbon resistor with a ceramic resistor ( which can get red hot ) etc. I personally know of a house fire caused by the latter. The owner had a timer on his bathroom vent fan which he repaired by replacing the burnt out carbon resistor with a high wattage ceramic resistor. No one injured, just a new roof.