Any old, worn out, and very floppy feather or down pillow.
Soggy Pillows can be referred to as "broken" pillows (i.e. broken pillows don't support the neck anymore and they bend right over the arm). They are usually old pillows over 5 years. An example is the feather pillow named "Big Mama" which is 24 years old.
Any old, worn out, and very squishy feather or down pillow over about 5 years old. Can also be referred to as a "broken" pillow that bends right over your arm and gives absolutely no support for the neck AT ALL.
I have a 24 year-old soggy pillow named "Big Mama." It is so pliable that it instantly takes the shape of whatever it's laying on.