@BFL
The wire is resistive, the wire induces a voltage drop
The battery is a resistance...this resistive load seeing a lower voltage will draw less amps
If the battery shorts out ...there will be no resistance except for the wire, The converter will supply full amps thru the thin wires until either the fuse blows, the wires melt, or the converter fails.. what happens will depend on the fuse and wire involved
Even so, if you connect a 40 amp converter with a short run of 16 ga wires and attempt to recharge severely discharged batteries the wire is going to dangerously hot
An inverter connected to batteries is not a resistive load..it is an inductive dynamic load and will draw as many amps as needed to produce the output demanded of the load it is supplying
If the wires do not meet the carrying capacity needed, they will melt if the batteries can supply the amps the load demands and the fuse does not blow
You cannot use voltage drop shut down as a safety control
Look at the nichrome wire used as the heating element in some electric heaters, small gauge wire carrying 12.5 amps 1500w...
Copper wire doing that would melt
All wire can be made to carry excessive current for small.amounts of time, but not safely and not day in day out