In N Out #5 Curb Alert

Price range: $5.00 through $20.00

Solve this riddle:
“Left to the Curb, no rightful holder,
A silent throne on city shoulder.
Its time has passed, life grows Colder —
When it’s the end, which word rhymes with closure?”

Riddle Revealed By Constantin Preda

the answer is the 1st word in the collection riddle.  can you solve them all?