Fancy Corners with Masks

[Acorn]

Even if the final result is destructive, masking is a good method to let you see real-time the desired result (minus the outline) as you can move around/change the cutout shapes.
As per Egg, steps 6 to 8 can be replaced with Select all and Substract shapes (Ctrl+2).

Boy that is useful.

Add back a Complete Stroke
1. Clone Masked Shape - Ctrl+K
2. Set Line Width to None
3. Detach Opacity Mask - Alt+O
4. Ctrl+Select and Delete any White Mask Objects
5. Select all and Arrange > Combine Shapes > Subtract Shapes - Ctrl+2
6. Ungroup
7. Add in Line Width

Acorn

[Boy]

Going through it once more, steps 2, 6 and 7 are actually not necessary.