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.