I think the motion of the slinky answers your question. If you think of the slinky as a number of coils. Each coil has gravity and the weight of all the coils below pulling it down and the coil above pulling it up. Except the top coil which has an external force pulling it up. When you release the slinky the internal forces between the coils stay the same and only the top coil falls. But, as it falls it releases the tension between it and the second coil, which then has no force holding it up and so on. In a way all dropped objects act like this. But for a more rigid object the internal forces adjust much more quickly so you don't see any change in shape. In fact, the idealised definition of a rigid body is that the internal forces are transmitted and adjust to the external force instantaneously throughout the body. The slinky is in a way the opposite of a rigid body.