Final answer:
The listing was most likely an exclusive agency listing, where the sellers are allowed to find their own buyer without owing a commission to the broker, unlike other types of listings.
Step-by-step explanation:
If a couple listed their home with a broker, and after two months they found a buyer themselves and were not obligated to pay a commission to the broker, the listing was most likely an exclusive agency listing.
An exclusive agency listing allows the seller to find their own buyer and sell the property without owing a commission to the listing agent. If the property is sold by anyone other than the seller, then the listing agent is entitled to a commission.
In contrast, an open listing allows the seller to have agreements with multiple brokers and only pay a commission to the broker who brings a buyer.