If you pause an automation (or make it "Inactive"), contacts remain in their action. When you resume the automation (or make it "Active"), contacts will proceed to the next action.
Timed waits
The countdown will continue running if the contact is in a “Wait” action.
For instance, if you pause an automation on day 29 of a 30-day wait, then activated the automation seven days later, contacts will continue to the next automation action. If you paused it on day 10 of a 30-day wait and reactivated it seven days later, they’d wait 13 more days and then continue to the next action.
Conditional waits
If you have a “wait until” condition that waits for 30 days OR a link click, and you pause it at day 29, and then reactivate it seven days later, the contact will be sent to the next action regardless of whether they clicked the link, because the wait timer has expired.