Should neutral and hot wire be tied together if not in use
No, these should be capped off as your picture shows.  If they are still live, code requires that the ends be in an approved box with a lid, and not concealed behind drywall or plaster (i.e. so the next person can get to it.  It looks like the conduit that brings the wires to the metal box has lost its nut to keep it attached to the box;  you should try to replace that too, so that the individual wires don't become abraded and short across the edge of the hole in the box.