What if there are more short positions than people willing to sell?

Assume that there are two traders, borrower (B) and lender (A) and both traders are at the same broker.

If (B) wants to short a stock, he borrows the shares from lender (A). If a lender (A) subsequently decides to sell his long stock, the broker will look at other accounts to borrow replacement shares so that (B) can remain short. If none are available, he will contact other brokers in an attempt to borrow replacement shares. If the stock is non borrowable, the broker will notify borrower (B) that he must cover the short position by 4 PM. If (B) does not do so, the broker will do a forced buy in.

The second situation in your scenario is the shorter's ability to maintain the margin requirement as share price increases. The margin maintenance requirement (MMR) is the amount of collateral (cash or marginable securities that must be maintained to support a short positions. It's 30% unless you're trading leveraged securities or your broker imposes stricter margin requirements. A margin call occurs if your account equity drops below the MMR. A simple example:

Short 1,000 shares of XYZ at at $13. The initial margin requirement is $6,500 which is 6,500/13,000. The equity is $6,500.

If XYZ rises to $15, the equity drops to $4,500 and the margin becomes 30% (4,500/12,000). If XYZ rises higher than $15, the shorter must provide additional margin. So it is impossible to hold onto the short position if the stock price is 100x. You'll be forced to cover or the broker will do it to you. Note that it is better to close the short position yourself because the broker will not work the position. He will just buy the shares in the after market when bid/ask spreads are usually wider, a disadvantage to you.