I apologize in advance if I have misunderstood the question. Please correct me if I have.
Placement records have fields that can and cannot be altered once the placement record is created. 'JobOrder' and 'Candidate' are two associations that are permanent once the placement is created either through the UI or through an API PUT call. New job submissions can be created and added against the job but a new placement will need to be made from it and the old placement either archived or deleted.
Here is some documentation on our REST API:http://developer.bullhorn.com/sites/default/files/BullhornRESTAPI_0.pdf