Yes, you can sell an interest in a debt; this is an alternative to paying a debt collection agency on recovery.
The contract that you have with the debtor may have limitations of the transfer of rights and obligations under the contract that may prevent this.
The value of the debt to the agency depends on the status of the debt and the credit worthiness of the debtor. If you have a judgement debt from a court, they don't come any more rock solid than that - the only limitation is the debtor's ability to pay. If the debtor has assets or a solid income stream an agency may pay 70-80% of the face value of the debt.