Err... objects with 100% self illumination cast shadows on other objects, they just don't receive any shadows. The stick on the left is 100% self illuminated. You might of turned off shadow casting for that object in the objects properties. Or turned off receive shadows for the ground plane? (Select object, right click,…
Oh in that case, copy the environment or create a small ground plane that follows the character around and apply a matte/shadow material to it. You probably turn off the shadow casting for the matte/shadow object, but leave receive shadows enabled. Works in a realtime viewport (shown below) and in renders.