Most tampon applicators are made of two or three pieces of plastic, but some are made of cardboard. Cardboard tampon applicators are generally said to be a greener alternative to plastic applicators because they can biodegrade. I had a hard time finding any information on the production of cardboard tampon applicators and how it affects the environment, almost everything I found was talking about the benefits. I wonder if the difficulty is, at least in some part, due to the lack of research and writing about the topic. One thing I was able to find was a paper about the impacts of various menstrual products, which mentions that chromium is something that is “emitted through energy use during the manufacture of raw materials such as cardboard, paper, and wood pulp via the combustion of fossil fuels”, and negatively affects plants.
There was more readily available information about the end of the cycle (pun intended). Cardboard applicators generally can biodegrade, if in the right conditions, however, the applicator is often put back in the (usually plastic) wrapper before being put in the trash, which would make biodegradation more unlikely. They cannot be recycled because they are “contaminated with menstrual blood”, so they end up wherever the trash for the specific building is taken. Even if they were able to be recycled, I think the likelihood of someone putting them in the recycling is low. I don’t often see recycling containers in bathrooms, and it doesn’t seem likely that someone would take just the applicator with them from the bathroom in order to put it in the recycling.