I posted a chain analogy elsewhere[0]. My understanding is that short interest being > 100% just means that the average length of the "short-lend" chain is greater than 1 "short-lend" pair. I don't think that such a chain is anything special - just that getting rid of the earlier short in the chain requires getting rid of the latter short in the chain first.
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Most stocks are head by the broker who combines them all into one listing of total number of stocks owned. This is all electronic, nobody ever worries about the actual stock behind it. When the company sends out a shareholder mailing they just give the company all the addresses, not how many shares anyone has. (I'm not sure how voting is handled!)
Note that there is a loophole above. It is possible to get the physical stocks personally instead of letting your broker handle it. This can force a short squeeze as your broker will be forced to unwind everything far enough to find real shares for you, and if required will force one of the shorts to buy back shares on the market. This has happened a few times in history, but few people have the means or inclination to pull it off (and it isn't what is happening here).
I'm by no means a finance guy and if I've misunderstood this, I'm happy to be corrected.