I think it is technically feasible to remove the box and leave the bed on the truck. I'm just not sure what advantage that provides.
You would have to remove the bolts that connect the front of the box to the front crossmember. You also have to remove the tailgate with the pivot mounts and the bolts that connect the rear of each side of the box to the rear crossmember.
You can leave the fenders connected to the sides. You would have to remove the connection between the fenders and the running boards and splash aprons.
The box itself would be pretty unstable because the only connections are between the front of the sides and the front panel. There would be no connection between the rear ends of the sides.
About anything is possible, but why would anyone want to go to the trouble of basically disassembling the bed while on the truck. The whole front panel would need to be unbolted, all the bolts thru the wood on the angle strips on each side (from under the truck), and while you could unbolt the rear cross-sill from the bedsides, they are also welded together, so you'd have to grind the welds off. Just pull the whole thing off the frame and do whatever work is needed on the bed, reassemble it, and reinstall it on the frame.
