Ugh, I can't show this well, but I will try.
If you have two circuits that share a common circuit protection device (fuse, breaker, link etc), the protection (or conversely wiring) must be selected so that a short in ANY conducter will cause the protection to become active and stop current flow.
Assume B+ is a battery and "FuseA" is a single fuse rated at say 30A
B+ FuseA(~)______Wire1_________Load"X"____GrndB-
B+ FuseA(~)______Wire2_________Load"X"____GrndB-
If EITER Wire1 or Wire2 becomes shorted to ground, it will fail FuseA, if the circuit is PROPERLY DESIGNED AND PROTECTED. With "home brew" repairs and projects, mine included, this is often not the case.
Again, EVERY conducter attached to a circuit protection device (fuse) must be capeable of carrying the amperage rating of the protection at all times. Or in reverse, the circuit protection on any circuit must be sized so that no wire connected to it will fail (melt) when carrying the full rated amperage of the fuse.
If a wire is "grounded" or "shorted" (to ground), it will try to carry the MAXIMUM current of the entire system. With a 225A batterty, that 16Ga wire will TRY and carry all 225A!!!!! It doesn't matter if there are 10 16Ga wires connected to that 15A fuse, the one that is shorted will carry ALL the load and fail the fuse.
The first part of the question was, I think, what if a B+ wire (wire1) chaffed to another B+ wire (wire 45) on a different circuit and would the resulting overload of the remaining wire (wire2) cause the fuse to fail. All GOOD questions and the answers are...... it depends!
Assuming wire1 is cut, leaving the entire load to wire2, if the circuit is designed correctly it will "pop" it's OWN 10A fuse, but in the example above, wires 1&2 SHARE a common 20A fuse. In that case, you fail the wire to the point of insulation melting and ultimately ground it and fai lthe fuse. LOTS of re-wiring to do!
Assuming wire1 is simply shorted to wire45 and wire45 is a power wire for something else. As long as wire45 and wire1 are similar in size nothing will really happen other than anything powered by one will also turn on the feature of the other. If the fusing is adequate, each wire will power it's load plus that of the other, whenever they are activated. In most cases, power circuits cannot handle much more than their own loads and the additional load will pop the fuse (or CB or link). However, this again assumes proper design where no wire is fused to more than it's rated ampacity, which with modified systems is often not the case.