Clyne spent five years on the books at Anfield, but only featured regularly in his first two seasons, with injury and the rise of Trent Alexander-Arnold limiting his chances.
It was inevitable, therefore, that the right-back would depart on the expiry of his contract, and the club did not even offer Clyne an extension to see him through to the delayed end of 2019/20.
Clyne, who had been training alone at Kirkby following his return from an ACL injury, quietly exited five years after signing in a £12.5 million move from Southampton.
Given his injury history, there will have been concerns for any club running the rule over Clyne ahead of a possible free transfer, and Palace manager Roy Hodgson challenged the right-back to prove his fitness in training.
Palace confirmed in mid-September that Clyne would be joining their first team for sessions for a short period, and having sufficiently impressed Hodgson he has now signed a short-term contract which is reported to run until January.
It marks a return to Selhurst Park for Clyne, who came through the ranks at Palace from under-8 level and made his senior debut for the club in the Championship, going on to play 137 times.
Liverpool have now seen the majority of the players released at the end of the season find new clubs, with Lonergan a notable exception.
Lallana joined Brighton, Pedro Chirivella headed to Nantes and Isaac Christie-Davies signed a deal with Barnsley, while Shamal George (Colchester), Kai McKenzie-Lyle (Cambridge United) and Niall Brookwell (Newcastle) have also landed elsewhere.
The Reds take on Palace for the first time this season on December 19, with a trip to Selhurst Park in the Premier League.