For your own protection I would make it clear and in writing with your client that although you will do everything possible using best practices there is no guarantee that you will be able to crush the negative sites completely.
What I have seen some very bad companies do is start to create a lot of indexed pages for their own site with a positive spin through
SEO and articles preemptively for keywords such as "scam", "ripoff", "problems" etc because they know they are going to generate problems. I would never do such business with such people but I am amazed how they know enough to cover their tracks for future problems they are expecting. I guess they had experience with screwing people and then having to clean up the mess.
If it is false information against your client you have other avenues as well.
If it is true what the ex employee is saying online and it is real bad showing they are dishonest you may want to consider who you take on as a client. I turn away more clients than I take on even though I can always use more. My clients know they can contact me 7 days week and I jump, wouldn't do that for someone I dislike or don't trust and experience has shown me people who screw others will eventually screw you - no matter how close you are to them