Anyone who shorts a stock whether naked or covered is responsible for all actions such as dividends during the period they hold the short position. If one trades options, one will see this reflected in the option price.
Would that mean the MM stuck in the short position needs to procure XMET to complete the transaction so whomever bought the shares was made whole when they cover?
Yes, and this is why GME skyrocketed. Hedges and MMs were DESPERATE to buy shares to cover this situation.
A squeeze is when it happens naturally; a trap is when it is intentional. Both use the same mechanism.