A new path? One that WE make and escape the Eye? It's giving Ghibli vibes again ^^
Six/New Lady got an Eye/music box tattoo when she returned to the Maw, having given up trying to escape her fate. I do remember thinking Six left the Maw at first/end of LN 1 to continue trying to escape the Eye's gaze (I guess the Nowhere now). But in the end/as she grew, she wound up just going back to end the hunger and pain she constantly felt.
She would build up the Maw again, bigger, more powerful, and more efficient then the Lady before her (and before her and before her), learn to use and harness her magic, and await the next girl to come and take her place. But after Mono/Thin Man's return, seeing he broke his loop (also effectively stopping a seventh girl from showing up), and her meeting with Granny, effectively proving that paths/cycles CAN change, she's decided she's not going to be pawn to the Eye anymore. She's going to destroy the Maw once and for all.