Pics always help.
I'd say yes the stud can be replaced. Remove wheel, brake drum, now support drum right at the stud that needs R&R, like a couple of deep sockets. The socket allows stud to drop thru but supports drum.
Now it's part number research time or match up at local auto parts store. Find the old grey bearded guy and ask him to match it.
To install, clean hole in drum for stud, insert stud. Now on wheel side put several washers over stud, apply a decent daub of grease on washer and in this case on the threads, turn lug nut or new same size nut on stud, now just start tightening the nut and maybe turn drum over and give the head a modest hammer tap if needed. Tighten until seated. Clean off the grease on the stud from installation.
Replace drum and tire and check that wheel torque several times to assure tightened to toque spec.
This link might help if a Dexter axle.