I’m not sure if I understand the question, but I’ll give it a shot.
If you made a request to a timeline without using since_id, and the most recent tweet you got back had the ID “abc” then, after some time has passed, you can use that most recent tweet ID “abc” as your since_id value to statuses/user_timeline. You would then get (up to 200) of the most recent tweets posted by that user “since” they posted tweet “abc”.