I keep food close to my broodies nest and take mine off of her nest daily never had a problem with dirty nest or hen not pooping but also she didn't lose as much weight either. However her nest has an A frame cover over it and the food goes under the cover which makes it within her reach
My broody just hatched her clutch. My recommendations is to put food and water within her reach from her eggs. Yes they lose weight but I haven't ever heard of one killing themselves by not eating. Best of luck