Mr. glupson
1. "How thin is that last connecting piece on the 0 AWG wire allowed to be before it can be considered a fuse?"
The 0 AWG is not for the current. It is for low resistance to match the relative low resistance of the amp. (DF). Some short and not so thin (I always repeated to use as thick as possible) wires at the end, won't change the cables resistance by much. Even a 12-14 AWG is no fuse. Most speaker cables on the market today are about that thick.
2. My two cents on fuse in Audio:
I don't think that on the amp – speaker's path, a fuse is a good idea. I would rather prefer some sought of electronic protection in the amp. This whole thread is about minimizing the resistance of that loop, so a fuse will not do well to that.
That fuse you are talking about, what is its purpose? To protect the amp from short circuit or to protect the speakers from a faulty amp.?
Most damage to speakers is caused by using a low power amp. that might go over derived (volume) to get it play louder. When that happens the amp. might go into clipping (saturation). That’s a situation when it runs from positive to negative saturation, causing a very steep transient (dv/dt) that has a nature of high frequency and high energy. The speaker's cross over passes it to the tweeter, that in no way can handle it and its very thin wire coil, fries. A fuse in series with the speaker wire won't protect your tweeters from that.
Most of my systems since I'm in this hobby, never had a fuse on the audio path. On the mains supply: yes.