"it is a mistake to allow assisted suicide. that will just open the door to forced extermination of anyone society feels is too old or too sick." this is an example of what type of fallacy?

This is an example of "Slippery Slope Fallacy".

The issue with this thinking is that it abstains from engaging with the current issue, and rather moves focus to far reaching hypothetical situations. Since no evidence is displayed to demonstrate that such extraordinary hypotheticals will in truth happen, this fallacy has the type of an interest to emotion fallacy by utilizing fear. 

It is meant that like tapestry scientific theories often need to pull out since they are not relevant and often times the whole chain of theories may be pulled out.