I'd rather it broke. If someone linked to the old URL, describing it as "the profile page of an international child murderer", and I later inherited that URL by signing up for the service, I wouldn't be too pleased.
The "y" example is confusingly simplistic; the site already has a "can't use duplicate usernames" rule, so 404'ing the original URL isn't 'worse' for anyone than if the original user didn't delete their account.
The URL isn't broken if it just points to a different resource.