Naturally it can happen. A lot depends on the elasticity of your skin. For instance someone that has spent a lot of time in the sun or is a smoker is probably going to be more likely to have saggy skin.
Drinking plenty of water helps prevent this also. A couple of times along the way I noticed what I called "chicken skin" developing on my neck, under the chin in particular but it "caught up" pretty quickly.
I also did some light weight work for the back side of upper arms to help prevent that from happening.
But no, never got that skin hanging off in folds like an elephant look.
Deb