Final answer:
The unexpired term of a member creating a vacancy is the remaining period of their official term in office. Temporary appointments may be made until a special election is held to fill the vacancy for the rest of the unexpired term.
Step-by-step explanation:
The unexpired term of a member creating a vacancy refers to the remaining period of time that the member was supposed to serve before their term officially ended. When a vacancy occurs, the executive authority is required to issue writs of election to fill such vacancy. However, provision is made via the 17th Amendment that allows state legislatures to empower their executives to make temporary appointments until the vacancy is filled by election, as directed by the legislature. The temporary appointee holds the position only until a new member is elected to complete the unexpired term or until the end of the next session in the case of recess appointments by the President.