Switch is wired Black in, white out, with metal box grounded. Test results show black to white- 0 voltage but ground to white or black- 120v. The box is fed from a 3 switch box on adjoining wall. I swear they forgot to wire overhead. There is no load coming from box. Wanting to install overhead can. Please explain and is it save? Thanks

What you have described is a switch loop. If there is no over head light, chances are that the switch controls an outlet in that room.

What HK said. This is very typical in homes of this vintage. The white and black are your line and load. Both are hots.

You'll have to find the switched receptacle and change the switch loop to a constant feed. Then you can run a new wire from the switch to the new light.

Another thing, you probably have ungrounded circuits in your home. You cannot extend these circuits, not unless you do some alteration, such as adding GFCI protection. And technically, since you are extending the circuit you must also now provide AFCI protection at the breaker panel.