Problem with character's falling down

Greetings !!!

I’m still rookie here so forgive me if I posted in the wrong section.

As you can see on the pics, when my character is on the edge, it does not fall down like it should be. Of course, when I move it a little bit more away from the edge, then it does fall down. However, I have problems when it comes to standing very close to the edges. Can you tell me what could be the possible problem ? Is it something with the animation or is a glitch in the design ?

Thank you for understanding! Cheerz!!!