Shorts enter by selling when sp is high, they buy

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Shorts enter by selling when sp is high, they buy later ("cover" when sp is low.

a) Seems that these 2 would neutralize each other, and sp in theory would net be unchanged after the cover (buy).
b) I'm guessing that when shorts come in by selling, that is what pushes sp down. If they coordinate with others, the effect is significant.

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Why the share price usually does not recover to its previous price is because the drop itself causes fear. But of course the shorts also put up a lot of BS to create more uncertainty. So what you have happen is not only are the shorts selling but also investors who are running scared who may never buy back in.

Then in some instances you have naked shorting where the short is on non-existent shares so they never have to be rebought to cover. Naked shorting is illegal but the SEC very rarely does anything about it.