Normally with a drop shadow you want it to work this way. The alternatives are:
1.) Extend the vertices past the bounds, then re-size the image into the bounds.
This solves the bounds problem, but lowers the quality of the sprite.
2.) Since you are just coloring the sprite Black, then moving it, you can just repeat this using a second sprite.
Duplicate the character sprite. Make it a child, give it a new canvas material, set visibility-> Self Modulate set this to black, move it. Done.
Now you have a second sprite acting as the shadow of the first.