Short term, the price spikes as the hedge funds collectively go "would you take $300? How about $400? $1,000? $10,000?" and eventually enough people sell.

If they don't (let's say there's no price they'd sell at), a few things can happen:

The short-seller can sell their short position directly (transfer liability) to someone who thinks they can convince the stockholders.

The Company can issue more stock, diluting all shareholders, and sell to the short-sellers.

The short seller simply goes bankrupt, at which point liability gets settled in court (details depend on how they shorted, middle-men, etc.) - other people like brokers could get dragged into this too as they may guarantee the trade.