The system allows naked shorting. There is no mechanism in the markets that prevent "leaks" because naked shorting is allowed.
There are brokers and market makers who "internalize" the market which essentially are local markets they create and handle themselves. Who knows what they are actually doing in those markets and how could one possibly limit naked shorting without some way to track all the shares? Even an immutable blockchain would not prevent this unless the users themselves could track their own shares and verify that they have legit shares and also so do everyone else.
So in the chaos of the markets there are nefarious actors(pretty much the entire market now) who counterfeit shares using various mechanisms such as FTD's, market maker exemptions, naked shorting, dark pools, etc.
As they increase the supply there are more shares out there than should exist. Generally this is hidden because no one is tracking it can there is no way to verify how many truly exist. Some experts including top executives in the financial system have suggested that over 50% of the market is fake.
But over time the shares change hands and events happen that can expose more shares than exist. The obvious example is when, say, a single person buys all the stock. If he buys all the stock and the stock is still trading then obviously there are more out there. E.g., The case of the guy who bought all the shares of a company and the stock was still having 50M+ volume per day.
How do shorters close out such positions? They just do. A shorter wouldn't necessarily know they are borrowing counterfeit shares. How does a naked shorter close out a position? Either they don't and just hope it becomes someone else's problem or no one figures it out or if they are forced to close it out then they buy back the shares they naked shorted.
If the SI is, say 100% of the outstanding then 1 fake share exists for every 1 real share. The naked shorters who ultimately did this(brokers not keeping track, market makers shorting to "provide liquidity", etc), to close their naked shorts, would only have to buy the outstanding(not 2x). How? They would have to offer a high enough price to get enough people to sell and not buy.
E.g., suppose the stock is trading at $1. If they offer $1M per share do you think they can entice enough people to buy back the shares to close out the naked shorts? Very likely. Of course they won't do it this way as it will bankrupt the world if the outstanding is high enough.
It's not complicated in the sense that if the price is high enough people will sell their "fake shares"(and every share they buy is a fake share w.r.t. to them). In some sense a naked shorter is just shorter who thinks they can get away without ever having to close their position... and usually they are right or get to close when the stock price has been tanked to near zero. But if a naked shorter is forced to be just a shorter then all the same rules apply.
The issue is this: Cheaters are not going to do what is right even if they are "forced to". They are going to find a way to maximize profits no matter what. E.g., a naked shorter who has to cover isn't just going to offer the highest price he can. He's going to spread FUD, hide shares, continue to naked short, etc. The system is designed to protect the cheaters because it is run by cheaters(ultimately the same cheaters).
So it isn't that they can't close it out. In theory they can. The issue is the cost to them in closing it out and who's going to force them and how hard it will be.
With GME, as you can see over 3 years later that they haven't closed out and have likely hidden most of the SI using various schemes such as hiding them in ETF's and using derivatives as ways to pretend they have covered.
The fact is this. If enough people buy GME: 450M buy 1 share and DRS, 225M buy 2 shares and DRS, 112.5M buy 4 shares and DRS, etc then IF GME has a large hidden naked short position it will expose the market and all the people who run it for the frauds they are to the world. In fact, the 450M number is far less because a lot of people already own GME. Also, as people do that and hold(or sell some at spikes and rebuy to own more for free) it only forces the naked shorters to naked short more to keep the price down because any big shorter position can implode causing a chain reaction or a gamma ramp.
The goal of the naked shorters/manipulators/financial terrorists is simply to drag this out and get as many people to give up as possible or to be made to look like fools. If RC somehow bought all the stock(when it was down in the gutter before the sneeze) then it won't matter. He's won't. It's like having a royal flush and having counting the shown cards to know that all the other players do not have one. You know you have the best hand and can't lose and everything they are doing is bluffing. [Of course they could resort sabotage to win such as murder, WW3, etc]
As someone once said: Every lie incurs a debt to the truth. In some sense every short incurs a debt to the longs. It may not be paid back in the same stock or maybe even in the same market or the same people but it is paid back in the long run(conservation of energy).
Here is a very good overview of naked shorting:
https://www.sec.gov/comments/s7-07-23/s70723-20162302-331156.pdf