If my husband signed a compensation agreement with a company but the

company is now pulling out of contract on, can we sue?

Generally, if the other side breaches or violates a contract, that frees you from performing under it: a breach by one party allows the other party to treat the contract as terminated. The breach must be a "material" or important one; in the context of employment contracts generally, that typically means a  breach in terms of compensation, benefits, location, seniority or title (if such were specified in the contract), but not something like specific duties done (since employers have a great deal of control over that, and the work you do can change without affecting the value of the job). In terms of non-competition agreements more specifically, unless the employee received some "consideration" (payment of some kind: stock, options, bonus, etc.) for signing the agreement, if the employer terminates his employment (i.e. he is fired, and does not quit or resign), that generally terminates the non-competition agreement, since employment was what the employer was giving him in exchange for his promise to not compete. Thus, without a separate payment for signing the agreement, if "all" the employee got was a job, taking away that job can be seen as both the employer breaching its obligations and as taking away the consideration which bound the contract.