If I had to hazard a guess, I would suggest that this rifle was originally chambered in one of the pistol class CF cartridges like perhaps .38-40 or .44-40.  If it were for one of the group that had equivalent CF and RF cartridges (such as .32 or .32 Long) it would have probably had the reversible firing pin, and a true rifle class cartridge would have most probably rated a forged action.  Anyway, that's my story and I'm sticking to it! 

Froggie

PS  I've still got some .25-20 SS ammo sitting on the desk next to my computer.  Do you ever get down to the Ohio Gun Collector's Show, or will you perhaps be coming to Louisville for the NRA meeting?  I could bring them to you at either of those. GF

I have four #2 Ballards with centerfire only breechblocks. This was common for a #2 if it fell into one of two classifications;
Either it was ordered in a caliber that was not made in rimfire and centerfire, or it had double set trigger option. 
One of mine is a .44-40, another is a .32-20, and the others are both double set trigger #2 Ballards.

Marlinguy,
It is just a loose action. I, of course, was wondering if it would hold a .25-20 SS chambering.

That's probably one of the few non original chamberings that I think would be OK in a cast #2 action. I can't imagine any reason why the .25-20SS would not work in a #2 action, if all things are in good condition, and properly put together.