A contact enters an automation only once
A contact enters a given automation once, ever. Re-subscribing or being re-added won't enroll them again.
A contact enters a given automation once, ever. Its trigger won’t fire for them again, even if they unsubscribe and re-subscribe or leave a list and rejoin. So a welcome series welcomes someone once.
Different automations are independent: the same contact can be in a welcome series and a win-back flow at the same time. To send someone through a flow again, build a fresh automation and target them.
See also Why imports don’t trigger automations and Why my automation isn’t sending.