If an officer cannot finish examining you at the border, you get a written order to leave Canada, and a copy goes to the carrier that brought you. It is not a removal order and it does not follow you forever: it stops having any effect the moment you come back to a port of entry and an officer starts examining you. Refugee claimants and protected persons sit outside this rule entirely.
(1)Except in the case of protected persons within the meaning of subsection 95(2) of the Act and refugee protection claimants, an officer who is unable to examine a person who is seeking to enter Canada at a port of entry shall, in writing, direct the person to leave Canada.
(2)A copy of the direction shall be served on the person as well as on the owner or person in control of the means of transportation, if any, that brought the person to Canada.
(3)The direction ceases to have effect when the person appears again at a port of entry and an officer proceeds to examine the person.