This happened to me some years ago in the UK. Fortunately, I had a good rapport with my customers, who knew me well enough to know that I would have informed them if I were to be stopping, so I didn't lose any.
If I had lost any, I would have either spoken to or written to every customer to reassure them of my intention to continue to work for them if that was their wish. This is what I would do today if it happened again.
Gary, I reckon you've probably got little to worry about. He's already cooked his goose by lying to your customers. If you have a good reputation with your customers he won't be around for long, if at all.
John