Closing a permit generally means completing the required inspections, corrections and administrative steps so the city's record shows the work as final or complete. Simply finishing construction does not automatically close the permit.
Building departments use their own terminology, deadlines and procedures. Treat this as a practical orientation and verify the current rule with the jurisdiction that issued — or would issue — the permit.
Check the issuing city's official permit record for a final, completed or equivalent closeout status.
Possibly, but the city may require inspections, documentation, new permits or other steps depending on the age and condition of the work.