The supply of shares for covering is not constrained by the number of actual shares in issue in the ordinary course of trading (you can create this condition artificially if you want to but people usually don't). There can always be more shares created for short sellers to cover with through shorting itself.

Short squeezes are usually not about supply constraints, they are about forced buying caused by margin requirements. High short interest just indicates a lot of potential forced buyers in the event of a price spike. Except in special cases there is particular magic to having 100% of the float on loan except that this is a high number which suggests many potential forced buyers under the right circumstances.