Hello, Rigging my first character but when I move the chest control on rig his chest kinda goes in self/faces fold up.
Welcome to BA 
I can see immediately what your problem is- you have flipped normals. To fix them, go to your viewport overlays, turn on Face Orientation, select anything red in edit mode, Mesh menu > Normals > Flip
Ah yeah in that case, Edit Mode > M > By Distance
Good for you for getting the number one problem new users to the forum have out of the way 
I’ve also tried this and no vertices get destroyed. ive tried with whole mesh which did delete some at a point that didnt destroy the whole mesh and have tried in just that area but cant get any to delete without deforming it.
Upload your file I will see what’s wrong with it.
Okay i will. Im at work but can when i get off
You need manually fix your weight paint. DEF-breast.l and DEF-breast.r bone weights should be smoothed in chest area.
Hm thanks. I was just weight painting the chest “bone”/control before which wasnt helping but the def bone seems to be fixing it