Anti-transaction replay in a hardfork

He cited an example of Alice paying Bob with an old-style time-locked transaction and asked why Alice would be holding onto such a transaction if she doesn't control any of the UTXOs and has no ability to substitute the transaction for one where she does control an output. He argued that Bob could still confirm the time-locked transaction on both networks after the hardfork under the proposed rules by sending the outputs to himself again with a different transaction format, making it a successful replay.