Basement – required to enclose and finish the basement stairs

I am finishing my basement, including enclosing the stairs: new treads, adding risers, drywalling in the sides. My question concerns structural requirements for the stairs.

Photos below for reference. (Apolgies for the junk on and under the stairs.)

Currently, the stringers are nailed to the joists at the top. The bottom of the stringers just sits on the concrete basement floor.

Other than at the top, the stringers are only attached indirectly:

a. On each side, about mid-way down the stairs is a 2×4 nailed into the joist at the top and into the concrete at the bottom. There is another 2×4 running horizontally between the two vertical 2x4s; it is nailed into the two vertical 2x4s and the underside of the stringers.

b. On each side, at the bottom of the stairs, is a 2×4 about 4' tall that serves effectively as a newel post for the handrail. The stringers are nailed into these 2x4s and the 2x4s are nailed into the concrete.

The stairway seems perfectly sturdy. My plan is to, basically, replace the 2x4s on each side of the stairway with a wall: Top plate, bottom plate and 2×4 studs. Then, I'll nail the studs to the stringers in the same way they are currently attached.

My only concern is that once I start messing with the stairway, the inspectors will require some major changes to bring it up to code (assuming it's not up to code right now for an inhabited room). (Note: I've looked through the applicable code–IRBC 2012–and cannot find anything on point.)

So, all that background for my question: Is it required that stringers be anchored to the floor at the bottom? Assuming so, will it be adequate to nail the stringers to the 2×4 studs of my new walls or will I need to anchor them some other way?

I'll appreciate any other thoughts you might have.

Thanks,

AEP