As computers increased in power, it became possible to do limited real-time physical simulations, which made death animations more realistic.
This had the advantage of low CPU utilization, as the data needed to animate a "dying" character was chosen from a set number of pre-drawn frames.
The term ragdoll comes from the problem that the articulated systems, due to the limits of the solvers used, tend to have little or zero joint/skeletal muscle stiffness, leading to a character collapsing much like a toy rag doll, often into comically improbable or compromising positions.
Recent procedural animation technologies, such as those found in NaturalMotion's Euphoria software, have allowed the development of games that rely heavily on the suspension of disbelief facilitated by realistic whole-body muscle/nervous ragdoll physics as an integral part of the immersive gaming experience, as opposed to the antiquated use of canned-animation techniques.
This is seen in Grand Theft Auto IV, Grand Theft Auto V, Red Dead Redemption, Max Payne 3 and Red Dead Redemption 2 as well as titles such as LucasArts' Star Wars: The Force Unleashed and Puppet Army Faction's Kontrol, which feature 2D powered ragdoll locomotion on uneven or moving surfaces.