There is not enough information to answer your question adequately. But here is my take on the question based on the limited set of facts.
If B signs a contract for purchasing a business believing employee C is part of the deal, whereas A does not believe that employee C is part of the deal, then it is a unilateral mistake. Whether the unilateral mistake is operative depends on whether A knows that B was mistaken in B's belief that employee C is part of the deal.
"A assures B ;that C will not work for another business, but is ill.": If this is untrue then this is a misrepresentation. A misrepresentation is an untrue or misleading statement of fact made during contractual negotiations inducing another party into the contract. There are three main types of misrepresentation, fraudulent, negligent, and innocent. Here, there are not enough facts to conclude either way.