Rag doll
This isn't an idiom. When you see AS___AS___you're dealing with A Simile. This simile is comparing something to a pair of old, patched socks, which would indeed be very limp.
simile its a simile when you use "like"
ANSWER:drowned kitten
Historically, the simile has been "deaf as a door post". *NOTE: Today, these kinds of comparisons would be seen as rude.
fiddle
mule
As dear as salt
Niagra Falls morning.
...mule."
as blue as sea
my teacher was as surprised as a dog
A simile. A simile compares two unlike items and specifically uses like or as in the comparison.