The answer is to do so carefully, for a few reasons. The first reason is that you can keep the upper hand and keep control of the messaging. Remember that employees talk to one another, and rumours can easily start to fly. If the circumstances are contentious at all then employees may be excitable, or confused, or frightened for their own job security. Informing them that a person is no longer on the team, and who will be taking over their responsibilities moving forward, can help keep things orderly.
If the departure is somewhat amicable, then allowing the former employee to have some input on the messaging may help them save face. Long-serving employees are usually particularly attached to their workplace, and so a sudden departure can be jarring for both themselves and their colleagues. Allowing them to even review messaging may help them to save face, and in turn may prevent hurt feelings from becoming a key motivator for any aggressive legal action.
