What happens if a coin-join round "fails'?
The vTXOs that would have been consumed and created by that coinjoin round are not consumed and not created. For the round to fully fail the ASP probably needs to spend the input they were planning to use in that round in another on chain transaction, which then gives the participants certainty that the coinjoin will never happen, and frees them up to spend their vTXOs in another round.
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Follow-up question.
What would happen if the transaction gets stuck in the mempool. Can the ASP do an RBF on the transaction or would it require all participants in the coin-join to sign the transaction again.
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The ASP cannot RBF, but could CPFP or pay a miner out of band to include a stuck coinjoin transaction.
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Eventually someone will need to use it as inputs and they're going to have to pay fees using CPFP, I suppose. Until then, Ark txs will be public so all participants in the round will have an incentive to keep it around to broadcast it if needed.
It does allow the ASP to double spend the input coins though as long as the tx is unconfirmed. Supposedly that can be mitigated by using one of the nonce-fixing strategies.