No, it doesn't. Imagine there is 1 share, owned by A. He lends it to B. B now (short) sells it to C. Now from C's point of view, he owns a share. So he lends it to someone. That person then short sells it.

So you have 1 share, that's shorted twice. But it's impossible for A and C to both have their loan repaid, because there's only 1 physical share.

Doesn't it unwind by just reversing the process? D buys the stock back from E and returns it to C. Then B buys the stock back from C and gives it to A.

That all sounds perfectly ordinary, as long as it doesn't happen on a deadline. If you tell D or B that they have to buy that stock right now at any price, they're going to take it in the (ahem) shorts. But if they were permitted to take their time, they'd buy it up at the market price, which would on average be pretty near the price they sold it.

It just so happens that there is a mechanism by which they can be forced to buy that stock right now, which is when F decides just on a whim to pay 100x the market price, and protection measures kick in. That's a screw-up on the part of B and D; they got sloppy and deserve to get raked over the coals for it. Everybody who wants to play that game needs to be aware of that scenario, and now they are.

But I don't think it's because there's anything impossible about having more shorts than stocks. It just takes an already risky thing and makes it super subject to manipulation.

Your link explains what actual naked shorting is, you should read it. It says nothing about re-lending.

Naked shorting is not "re-lending", it's a very specific technical thing where you sell the stock without owning or borrowing it at all. Naked shorting results in failure to deliver.

Stock trades settle a couple of days after execution, so what it means in practice is that Alice "buys" the stock from Charlie, then 2 days later when settlement should happen and the share and money are supposed to actually change hands, Charlie goes oops I don't actually have the stock. Then the trade is undone.

In effect Charlie duped Alice into a fake trade that artificially depressed the market price.

It's an egregious market manipulation tactic and has nothing in common with the practice of lending or re-lending shares, in fact there is not a single share involved at all.

If you fail-to-deliver enough you'll get booted by other market participants and/or the SEC.

No, it doesn't mean that. The same share can be borrowed more than once. If A borrows a share from B, who borrowed it from C, the same share is shorted twice without naked shorting.

No. Re-lending and naked shorting are nothing alike.

Actually my example kinda sucked. What's more likely to happen is that B borrows the stock from A, then sells it to C.

C then lends the share to D.

C doesn't know or care that the share was already borrowed once, and the only way to prevent re-lending it that way would be to make shares non-fungible, which would break more-or-less everything (then again maybe that's your goal).

You can recall the shares you lent anytime. So if A borrows shares to short, and lends them out to B so B can short, if A wants to close their position they can tell B to give back the share. Not naked even though A has reloaned the share.

How do you short ? You short by borrowing a stock, and selling it. Why would lending it instead of selling it be a naked short ?

No. Person A has 100 stocks. Person B wants to short the stock. So Person B, borrows 50 stocks from person A and sells it to person C. The float is now > 100%.