What happens to his transaction after? It will simply burn fees and get back to his wallet (automatically?) or or his transaction will stuck someone in blockchain and he will have to spend extra funds to move or accelerate it ?
By default, Bitcoin Core nodes drop unconfirmed transactions after 14 days; not 7 days. Once the transaction is dropped, the sender is not charged anything and can spend the same UTXOs again. However, the transaction could be broadcast again by anyone in the future, so invalidating the transaction by spending one of the transaction's inputs should be considered.