Should I connect the ground to the box when relocating a dryer to the basement?
The risk with not grounding the box would be the hot wire touching the metal, and with no ground the breaker won't trip, this could result in it grounding through you if you touch the box (electrocution). Some outlets are "self-grounding" where no bonding wire is needed for the box. Check the outlet to see if it is self grounding. You can add a screw to the box for a bonding wire if not. After installation, check with a meter- one lead in a hot receptacle and the other lead touching the box, if the meter reads 120v, the box is grounded.