The former owner sold the business for a reason, so I believe the former owner should only stay for a short amount of time. Most of this time should be to answer questions, sign over any miscellaneous items that may have been missed, and be available for issues that may come up for the first quarter or so.
This owner has put his or her life into the business, so any change that the new owner makes is going to have an effect. If I had to guess, 95% of the time, the old owner will not be happy with the change.
It’s better to have the old owner leave so the employees can get aclimated to the new environment without feeling like they are being disloyal.