Help with a 3d model on blender

Hi, I’m new in blender, so I’m going to explain my situation as well as posible.

I’m trying to create key shapes on 3d model (for talking animation for example), to after import to unity. I’m getting mad, because I import my fbx model and when I select edit mode ocurrs that the part of the model turns down.

Here is an image:

How can I fix it?
Thank you.