Hi Tiffany. It can be confusing sometimes. Sl lineare is one that goes dormant or semi-dormant in the winter months. I would not clean it up until it starts actively growing again.
I am also in zone 8b here in the Willamette Valley, OR. Try looking up your sedum in our database and look at photos with dates. That might be helpful in seeing which ones will go dormant.
Can you tell us how you are growing your S. lineare, what type of soil, how much water, how much sun? A photo would be helpful.
Here is a photo from springcolor showing lineare in a dormant stage.