A "Sawdust Woody" is a slang term used to describe a false erection that appears visually idyllic but is actually soft and pliable when examined. It's a "counterfeit erection" that may occur due to various factors such as anxiety, medication side effects, or medical conditions.
*Becky to a friend* Wow, Elrond really ended up having a Sawdust Woody - very disappointing.