Why does defeating ISIS mean that you have to kill the ideology? That's two different things
+1
The Nazis were defeated though their ideology lives on.
The Nazi ideology that lives on today means hardly anything because in order for it to be effective it has to be in coordination with too many; whereas the ISIS ideology can be followed by loners and carry out attacks on their own in the most remote parts of the globe.
Actually, that itself is their ideology - to fight for sharia/shia wherever, whenever and in whatever circumstances, whether you're alone or with others.