Redemption is the arbitrage channel that makes a peg hold. If a token can be redeemed for $1 and trades at $0.99, buying and redeeming is profitable, and that buying pushes the price back up. Without a working channel the peg rests only on sentiment.
The details decide whether the channel functions in a crisis. Minimum sizes are often $100,000 or more, accounts require kyc and can take weeks to open, fees apply, and issuers generally reserve the right to suspend redemptions. A channel that closes under stress is not a channel.
This is also why depeg depth varies. A token with wide, working redemption tends to snap back within hours; one where the only exit is selling into a liquidity-pool can stay dislocated for days because the whole market is trying to use the same thin path out.
Related: depeg, fiat-backed-stablecoin, stablecoin-attestation, price-impact