1960s light switch issue wiring
the screw should thread directly into the wall of the box (there is no nut that may have fell away). To check that the screw isn't stripped try turning it without the wire bracket in place. If it doeesn't want to thread in easily look at the screw threads and confirm they are intact and not stripped or damaged.
If they look damaged replace with a new &quot;round head machine screw&quot;. I believe the thread size is a 10-32 x 1 inch (it may be 8/32?). Bring it to the hardware store and match it.
If the threads are damaged on the back of the box purchase a self-threading screw slightly bigger and drill it into the original hole.
If you'd rather not attempt the repair your self (always good to know limitations) there is a very low chance of any hazards occurring until an electrician arrives. the clamp is used to prevent the cable from being yanked out of the box and there is probably a cable staple close to the box as back-up.