Final answer:
The element of accountability described by forces that spend at least one night in temporary lodging but are assigned elsewhere is known as 'Transients'. This concept is crucial in military operations for maintaining effective personnel tracking.
Step-by-step explanation:
The forces that spend at least one night in billeting at a location but have their final duty location elsewhere are described by the Transients element of accountability. These individuals are accounted for differently from those who are assigned to the location permanently, as their stay is temporary.
The concept of accountability for transients is especially relevant in military contexts, where the orderly and precise tracking of personnel is critical for operational effectiveness and security.