No, they do not. A fixed term contract is a contract with a pre-set expiry date, which can run for several months to even several years. When an employee signs that contract, they enter into the agreement with advanced notice of their end date, and a knowledge that they will need to start looking for work when the contract is complete.
The law changes, however, if an employee is let go before the end of their fixed term contract. When that happens, there is judge-made law from various provinces stating that the employer will owe the former employee money from the entire duration of the contract, and the employee would have no obligation in that case to mitigate. While fixed-term contracts may look enticing, they can actually be far more expensive in the long run.