Usually, swans will leave to join other swans during the migratory season. However, if the swans are pinioned (portion of one wing amputated so they cannot fly) or the feathers are clipped on one wing so the birds cannot fly, then obviously, they will not leave their resident habitat.

If the swans are captive and unable to fly, they usually will stay in their resident habitat unless they are chased by a predator or they start searching for food or other habitat resource that is no longer available. The Regal Swan