So I started looking up the numbers on this. Yes, the short-seller has to have collateral equal to the full market value of the short position -- but they actually have to have more. When opening the position, they need an extra 50%. (Note, when opening it they do get cash for the initial sale so that covers the "full market value"). So when our example short-seller opened the trade, they needed "extra" collateral of $122.5K, for a total of $367.5K
In order to maintain it, they need an extra 25% by NASDAQ regulation, but almost all brokers require 30% or more. On volatile stocks, like Tesla, they often require even higher amounts. If we assume the 30% requirement, then at $300, they need $330K of collateral. Our sample short-seller isn't dead yet...
But, for example, consider someone who was short 1000 shares at the beginning of January, at $213.69. This position has a value of -$213,690. They must have started with collateral equal $106980, plus the short sale proceeds of $213960, for a total of $320940. At the current price of $303.70, and a 30% maintenance margin, they need $394810 in collateral to maintain the position. They need to add $73970 in collateral. This is a margin call; if they don't wire the funds in, the broker will close their positions for them. (Obviously most short-sellers would have started with excess collateral for safety, but you see the mechanics here.)
The thing is, certain stocks have higher margin maintenance requirements. For instance, last I checked, Tesla has a 50% maintenance requirement at Schwab if you want to hold it on margin "long". I just checked and the requirements for holding it "short" are just as hefty -- 50%.
In this case, this is pretty brutal. If we assume a 50% maintenance margin, our hypothetical short-seller who shorted at the beginning of January has had to add $135,010 of collateral (1.5 times the change in share price). Note that they started with $106980 before making the short sale, so they've already had to throw in 1.3 times as much money than they initially invested.
I don't know if we can generalize from Schwab, but if this is the maintenance margin level for TSLA at most brokers...