If you've run into an issue where you've created fabric clothing or hair or etc. and it seems to completely ignore the movements of your animated character, take a look at your modifiers:
Modifiers are applied to your animation in order - starting from the top and going downward. If your armature modifier is placed below a hair or cloth modifier, then the movement will have no impact on the hair/cloth.
To reorder your modifiers:
Make sure the modifier is toggled open (instead of closed like the image on the left)
Click on the up or down arrows on the right to change the order (repeat as necessary)