Shredded memory foam pillows, or pads disguised as pillows, are becoming popular with many consumers due to their firm yet the comfortable structure and their ability to provide a cool surface on which to sleep. Shredded Memory Foam pillows are great because they are comfortable to sleep on. The downside is that they can sometimes have a strong smell. Shredded Memory foam pillows typically have a problem with dirty sweat, which is why they so often give off a stinky smell.