The Falloff object is a special object that allows the user to set a specific falloff to a joint as a separate object.
This has two advantages: First, it allows an area of influence to be defined that can deform the object based on the position of an object other than the joint itself (useful if you need to add some extra deformation only when a chain of joints reaches a certain state, for example); second, it allows you to bypass weight painting altogether by using the Falloff function of the Falloff object as your area of influence.
Assigning a Falloff object to a joint is pretty straight-forward:
Once done, you can easily see which Falloff object is assigned to which joint, since each Falloff object will be shown as a Child of said joint.
Since the Falloff object is not a deformer, it can be placed anywhere in the hierarchy, much like joints. Only the Skin Deformer needs to be placed as a Child of the mesh to be deformed.
Keep in mind that moving or rotating the Falloff objects alone will not deform the mesh. They are tied to joints, so only joints can actually be used to deform the meshes. Falloff objects are only spatial falloffs and define the area of influence of a joint. While they can be moved separately from the joints, only the area of influence of the joints will be changed when doing so (in other words, the mesh vertices are tied to the joint. The Falloff object defines which area of influence the joint will have on these points).
While limited, this is still useful to check out the influence of a Falloff object, as the falloff gizmo in the editor view can sometimes be hard to read, especially if a lot of Weight Effectors are used.
While Falloff objects can be used without actually painting any weights manually, you can still do so if you wish. In this case, the Falloff object will be used to fine-tune your weighting, or to better manage transitions with other joints.
Falloff objects can also be baked easily by opening the Weight Manager (hold
Falloff objects can also be used as spatial limits for other objects, e.g., Voronoi Fracture objects (see Falloffs).