The actual improvement (physicaly and musically) of a piece we memorise never stops. So we could get philisophical and say we never actually completely finish a piece. However I think it is not the right way of thinking because we are actually improving an aspect of our playing as a whole as we maintain contact with our memorised repetoire.
....it would stop idiots from saying they have "mastered something" you may "get" a piece of music, but saying you have mastered it is putting a pretty big ticket on yourself.....
"perfection" is unattainable perhaps because it does not exist at all in anything inherently subjective.