When I found these in my yard, I thought I knew exactly what they were. Terrestrial snail egg cases!
They looked much like the tulip snail egg cases below which I had found earlier along the shoreline.
However, upon further investigation, I found that the photos at the top of this article are of birds nest fungus (Cyathus stercoreus). Birds nest fungi have their spores in little packets called peridioles.. The soft flexible "bodies" extending from the peridioles are an attachment to the side of the cup that deteriorates as the fungus develops.