If you cancel your Apple Arcade subscription and then later resubscribe, can you continue your games where you left off? Let’s say I end my payments and then resubscribe later. My concern is to continue my games where I left off once I start paying again. 

Basically, does cancelling the subscription preserve game data or remove it?
Yes.

As per the Apple Support document:


Access your Apple Arcade gameplay data on all of your devices:



  If you cancel Apple Arcade
  
  If you cancel your subscription to Apple Arcade for any reason, you can resubscribe and still access your gameplay data. If you wait too long, some of your game saves might not be supported by the time you resubscribe.
  
  If you're not an Apple Arcade subscriber, you won't be able to play any Apple Arcade games, even if you downloaded them to your device. Delete the apps if you don't need them anymore, or resubscribe to keep playing.