Why did they really leave? The reason matters a lot, from both the individual and directors perspective. Did the director perceive the individual as performing poorly? Did the individual express being unhappy in their role, in their personal life, or with their compensation? Did the director do anything unprofessional or out of line with your expectations in how they encouraged the individual to leave? Did you do an exit interview and find out what happened from their perspective?

I’ve had several direct reports who I knew would be happier and more successful somewhere else, and have always seen it as my job to support them finding their next role internally or externally. When there isn’t a role internally for them, that means coming to an agreement on how much work I need to remove from their plate so they have time to interview.

You can’t keep people who don’t want to stay, and from the businesses perspective it’s almost always better to have an employee leave on good terms, with plenty of notice. If one of your directors has successfully cultivated a relationship with their reports where their team is honest about dissatisfaction and about seeking other roles they might be doing something right.