What's your jurisdiction? The rule that a corporation must be represented by an attorney is jurisdiction-specific -- that is, it's not a universal rule. For example, in California and New York, the rule does not apply for small claims court but does apply for other civil lawsuits. So, your first step is to determine whether your state (or the particular court in your state) permits corporations to represent themselves without an attorney, and if so, in what instances. Sometimes lawsuits are permitted if the corporation is represented by a director, officer, or employee of the corporation.
Can the "right to sue" be sold? There are many legitimate ways to transfer a right to sue someone. If the right to sue arose out of a contract, those contract rights may be assigned (unless the agreement prohibits or eliminates assignments). Similarly, if the lawsuit is over a debt or an existing judgment, that may be assigned, as well. Many jurisdictions prohibit "champerty," the funding of, or investment in lawsuits and "champertous connivances," (scroll down to P. 165) are rare.