I think you are dealing with tapeworms. In the case of fish or beef tapeworms - there is only 1 "mother" parasite that can grow to be 30 feet long or so. Tapeworms are called flatworms because they are very flat - just like a ribbon.
In the case of canine tapeworms - there are more of them - but they only grow to be about 9 inches or so.
Both types of tapeworms are made of segments. Each segment has both male and female reproductive organs - these mate and the segment fills with eggs. Once full - the segment will break away from the "mother".
When a tapeworm dies - it dies from bottom to top - this is why egg sacs will be seen first - then longer and longer pieces of the parasite. The pieces will be flat.
The head of a tapeworm only serves to anchor it to the inside of the body.
Liver flukes come out whole as they live their entire lives in bile and acids do not affect them.
Pinworms are the most easily spread follwed by roundworms and tapeworms last. The toxins put off by parasites are what causes the illnesses associated with parasite infections. Only hookworms drink blood.
Wash your hands after using the restroom and before eating and disinfect the toilet daily when parasite cleansing.