Small Business Divestiture - Early Questions?

I have a proprietary deal specializing in specialty cleaning for restaurants that I really like, however, this would involve the owner spinning off this division of the company as a standalone business and continuing to operate the existing business in the other verticals.

Are there any key questions to ask or special considerations for an SMB acquisition when it is a divestiture instead of a full sale? If I'm not getting the existing company's name, is there commonly a price discount? Since it will require some level of future interaction and partnership, what are the top points to align on early?