Any company seeking to manage transitions smoothly should always have people waiting in the wings in the event of a departure. Continually training and preparing your staff to move up in the company, either with more responsibility or more pay (not necessarily tied together) keeps your company ready for any transition.
The complaints I hear from people about having a transition process like this are “if I train people to do more, they will get a job elsewhere” or “if I train people for a promotion and they don’t get it, they will be dissatisfied.”
It’s better to have an over-trained team than one which lacks skill or personality. I’ve worked for companies who always were smart about transition; at any time, these companies always had someone who could step in in the event of illness, resignation, or change in volume of business.
As for the departing employees themselves, it is important to get a “data dump” from them before they leave and perhaps hire them on as a freelance consultant as needed to enable the transition process to proceed properly.