Respawn is implementing penalties for players that are leaving arena games that have not yet finished.
Respawn to Crack Down on Leavers in Apex Legends Arena Mode
The system will work just like the penalty in the ranked battle royal mode, meaning you will only recieve the penalty if you are apart of a full squad when you leave, so if a teammate who is not partied with you leaves and you are at a disadvantage and don't wish to continue, you will be safe to leave the game and not face any penalty.
Penalties for abandoning games have been added to Arenas. This is similar to the abandon penalty applied in Ranked BR games. You only get the penalty if you were in a full squad when you left (this doesn’t apply if you were partied with the leaver—you’ll still get penalized in that case). This update will activate a warning for players who are about to leave a game in-progress. The associated penalties will follow shortly after.
Read more: Apex Legends Patch Notes - May 24 Update.
The Arena mode is a new game-mode in Apex Legands: Legacy and features 3v3 style gameplay like you see in a traditional team based shooter with all the quirks that come with a battle royal and Apex Legends.
Players are still asking for a ranked arena game-mode and these changes could be a step in that direction.