Parasitism is an association in which one organism, lives on another, the host, deriving benefit from it and causing harm to it.
The tapeworm here is a parasite and it lives inside the cat's(host) body where the tapeworm is specialized for its mode of life. It survive and reproduces very well without needing another specie because it is a hermaphrodite. It causes loss or poor development of unwanted organs such as the digestive, sense organs and muscles. Its long flattened body also provides a large surface area for absorption of nutrients too.
The importance of ecosystem stability is that if the ecosystem is not stable then it cannot survive. A current example of an unstable ecosystem in the Amazon Rain forest. It has been delt so much damage that it is begining to self destruct and kill itself as well as emit greenhouse gases instead of slowing them.