Can a contact enter an automation campaign they haven't exited yet?

Yes.

Depending on your campaign's re-entry condition, exit condition, mutual exclusivity and the contact's behaviour, it's possible for a contact to enter a campaign which they are already in.

For example:

In this automation flow a contact enters when they place an order.

The re-entry condition says they can re-enter again after one day - so if they place a second order a day later, they could re-enter the campaign before the entry wait has passed.

You can always choose not to allow re-entry if you want to stop this happening, or use frequency caps to stop your contacts from getting too many emails from you.