Why ascaries eggs are bile stained?

The bile pigments (bilirubin) are excreted by the liver and enter the small intestine as components of bile. Here they undergo bacterial degradation of bile pigments by the bacterial β-glucuronidases, giving rise to urobilinogen, which is further degraded to stercobilin.

Ascaris lumbricoides lives in the lumen of the small intestines, hence it is not subjected to the action of bile pigments (that act in the small intestines). So Ascaris lumbricoides do not come in contact with bile pigments and hence their outer covering does not get bile-stained.

The bile-stained eggs refer to the eggs of the liver flukes (Fasciola hepatica). Eggs of Fasciola hepatica are bile-stained because when the mature worms live in the bile ducts, the bile pigments enter their uterus and stain the freshly laid eggs.