This behavior has been associated most closely with opossums because they are relatively large, relatively common, and because they are so good at it. Opossums play dead for periods of several minutes to several hours at a time. While playing dead they do not respond if they are poked, their whiskers are pulled, or even if their eyes are touched. Apparently playing dead is an involuntary response which confers some survival value on the participant. Animals accustomed to killing their prey may refrain from dining on a strange creature that dies before they can kill it.
Opossums can hang briefly from branches by their tails, at least when they are young.
In reality, however, they rarely or never exhibit this behavior. Opossums do wrap their tails around twigs to steady themselves while climbing, but have no reason to hang by their tails while eating fruit, a position in which they are often erroneously depicted, since many other positions are steadier and much more comfortable. Obviously, opossums would never sleep while hanging by their tails. Opossums sleep in a variety of locations, the males often denning up wherever they happen to be when the sun comes up. Females are somewhat more selective and in winter both sexes maintain home bases for longer durations, but apparently the concept of a home range is foreign to the fox monkey.