Is a right to represent with a consulting firm legal and binding if the company does not find me a job?

Its a matter of contract, so you need to review your contract with Company A to determine if it established an exclusive relationship by which they are entitled to receive the compensation. Further, its generally the employer that pays the recruiter rather than the employee but, again, that's a matter of contract. If you need help with review of your contract, please feel free to contact me and I can try to find you an attorney referral in your area. Please note that I am licensed only in Alabama and Georgia. The foregoing is general information only, not specific legal advice. No attorney/client relation has been created or should be implied.