Does the mesh influence how well you can retarget an animation?

I have retargeted an animation to another rig successfully. In the image you can see an example of two characters executing a sliding animation on the ground. The animation was made with the mesh+rig of the character on the right. The very different character on the left is a cute biped humanoid with a much thicker mesh. When the cute character does the slide you can see it pierces the plane. Is this something that can be fixed by modifying the cute character's rig (either in Unity or by modifying the source) or does the significant difference in the mesh make it impossible to use this animation without editing it to be used by it? For a walking animation, and so-on, the retargeting has no problem. But its these special animations where the hip bone gets close to the ground that it doesn't work.