Does the curvature tool need to create a closed space before it can be shut off?
You can click the Esc key or just select a different tool to end the path.
Or, if it drives you crazy, turn off the Rubber Band for the Curvature tool in Preferences > Selection & Anchor Display.
If you hold the Command/Control key and click with the mouse it will stop the drawing of the path. This works with both the Curvature Tool and the Pen Tool.