No. If tenants are sharing a rental property and each paid part of the security deposit, the landlord is under no obligation to return part of the security deposit if one tenant moves out early. The security deposit is usually only returned when the tenancy ends. When the security deposit is returned at the end of the tenancy, the landlord must make the cheque out to all of original tenants named on the lease, even if one of the tenants already left the premises.
If the landlord does agree to return some of the security deposit early, this agreement should be put in writing.
Tenants may also want to consider creating a roommate agreement to specify what would happen to the security deposit if one person left early. A sample roommate agreement can be downloaded here.