Hi Jaden.
I’m not 100% of the set up you are using but let me take a stab at solving this for you.
I think you have a character with is the letter “I”, which sounds like should be rigged, and it is holding a pixaxe which is rigged.
If the “I” character is just using a blend shape to deform and you have parented the axe to it, then it is just going to stay in its position relative to the object which is probably not moving. (even though the verts inside the object are moving).
You could do a 3 vertex parent rather than an object parent if that is the case.
However, if your “I” character is rigged with an armature, you can parent the axe to one of the bones inside this armature and then it will move relative to that.
Maybe you can post a video if you need to explain more.
Hope that helps.