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Investors who short a company might get into trouble if a group of passionate online day traders (who like the shorted company) decide to boost its stock value by coordinated investments.
How quickly can the investors who shorted the company back out of their short? If they can convert their short to a “long” immediately, then isn’t the damage minimal?
Or does the speed of information effectively wipe out the short advantage, causing maximal damage prior to backing out?
Let us first set the scene. When a market participant $A$ is shorting a company $X$, he is effectively going to see some other participant $B$ who holds shares of company $X$ and borrows these shares from him (in exchange for some interest). $B$ delivers the shares to $A$ with the agreement that $A$ will eventually return the shares to $B$. Once $A$ receives the shares, he can actually sell them in the market at time $t$; if the stock price of $X$ goes down, he can then repurchase them at a lower price at time $t^\prime>t$ and return them to $B$. The difference between the sale price at $t$ and the repurchase price at $t^\prime$ is $A$'s profit (or loss).
Now to your questions.
How quickly can the investors who shorted the company back out of their short?
As you can see from the previous explanation, for $A$ to back out of its short position, he needs to buy back stock from the market. That means the more liquid the market is, and in particular the more supply of shares there is, the easier it would be for him to close his position. Now, regarding recent events, you are probably thinking about GameStop. One of the issues that seems to be happening here is that short interest as a percentage of free float is above 100%, see this article. Free float refers to the amount of shares hold by market participants willing to buy/sell them (as opposed to large investors that have stakes which they do not intend to sell). In this case, closing a short position should be extremely tricky, because there might be too many people trying to close their short (i.e. buy back the shares) with respect to how many shares there are on offer. This is known as a "short squeeze" and contributes towards pushing the stock price upwards, because demand for buying outstrips share supply.
If they can convert their short to a “long” immediately, then isn’t the damage minimal?
To shift from a short position to a long one, $A$ would have first to buy back shares on the market; deliver them back to $B$ (to close the short position); then buy again more shares on the market to open a long position. Again, the crux of the matter is liquidity and share supply: the more share supply there is, the quicker $A$ will be able to close his short position, the less loss he should incur. With little liquidity and multiple participants seeking to close their shorts, closing the position can take time and the price will be trending upwards because of the supply-demand imbalance, which can get quite painful for the shorts if there are enough of them and those holding shares don't want to sell...
Or does the speed of information effectively wipe out the short advantage, causing maximal damage prior to backing out?
Bear in mind that what is happening on e.g. GameStop is highly unusual. Generally speaking, if market participants "smell blood", well you can expect a bloodbath. In this case, the developments in GameStop's share price have made it to the news, and rather quickly for that matter. Other market participants might look into the situation and evaluate what is going on. If they conclude those holding short positions are effectively in a very precarious situation (that is, they are still struggling to close their shorts), they might jump into the wagon, expecting further buying pressure, and open tactical long positions to benefit. This contribute further towards upward pressure for the stock, creating a vicious (or virtuous, I guess it depends on your view) cycle.
At this point I believe it becomes difficult to foresee how the share will evolve, with further technical factors muddling the picture (e.g. passive fund providers having to buy the stock to replicate indices, etc.) and, I guess, even the expectation that the SEC might suspend GameStop's shares to avoid further "disorderly" trading.
So those were my 2 cents. Hope it helps. Maybe someone else can provide further details.
The answer is really quite simple and it requires no fancy formulas. Orders are filled by price and time priority. You can close your short as fast as your order gets to the front of the order book.
IOW, if you place a market order to buy (to close) then all market orders received before your order will get filled first. The problem is that since it's a short squeeze, price could be gapping up points per minute or even per second (see Gamestop) and how high a price you will pay will depend on how on fast the sell side liquidity clears out all of the buy orders ahead of you.
