It is an understandable fear that patients either leave and find another dentist once you take over or they follow the departing principal to where they might still be working.
To deal with the second point first, this should be covered off in your sale and purchase agreement giving you recourse to the seller if they continued to treat patients after they sold to you. After all the goodwill relates to the patient base and ongoing delivery of treatment to these patients.
With regard to patients leaving to find another dentist, this tends to only happen where patients have already moved away, and the change sparks them to look for a more local dentist or they have been unhappy with the practice prior you taking over. Either way the numbers are small. Most patients will give you the benefit of their custom and it is for you to prove them right for putting their trust in you and your practice.
Ensuring patients have a good first experience under your ownership tends to result in the overwhelming majority continuing to be patients.
If a few do decide to leave you may not have been a good fit and developed a good dentist-patient relationship so it may be a blessing in disguise.