I know there is a word for this!
Person A is a seller. Person B is a buyer.
Person A is worried Person B will take the her product and not pay. Person B is worried of the inverse.
These two hire an unbiased Person C to mediate the transaction by taking the money from Person B and products from Person A and only releasing either item when both items are held by him.
Many words that seem like they would work, such as mediator, seem to be very general: "to make people involved in a conflict come to an agreement."
I am hoping there is a more specific term for this situation.