Student always tend to forget that a solution must remain electrically neutral by all means. If you want a certain ion to leave water, you must provide another ion of the same charge that has left the solution.
As per discussion in the comments to that answer, is the second quoted sentence strictly true?
Can electrical neutrality not be achieved by electrons (rather than ions) migrating one way or another to provide balance? For instance, perhaps imagine an aqueous solution under electrolysis which is divided by an appropriate membrane. A quick search brings up AEM (Nature paper) which appears to depict unidirectional migration of hydroxyl ions.