It's a song. It's poetry. Poets take liberties with language.
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Jigsaw Puzzle -- Note that the puzzle consists of many pieces. This puzzle is unfinished (undone).
The song writer is comparing her life to an unfinished jigsaw puzzle.
She is trying with great effort to complete the puzzle. (Trying ... to fill the emptiness.)
There is a piece missing from the puzzle. (The piece is gone.)
So the puzzle is unfinished. (The puzzle is un