There was a recent Holmes on Homes show that covered this exact topic. In that case, the cement used for the poured foundation had too much water added when it was mixed and the foundation walls were crumbling - causing the house to sag.

To fix it, they built a new foundation wall on the inside of the house all the way around the perimeter of the basement. They poured new footers, and then used cinderblocks to make the walls. At the top of the wall, they installed a wood header to the joists and then filled in the gap between the top of the cinderblock wall and the bottom of the wood header with a non shrinkable grout. There was a lot more involved to deal with the water seeping through the old foundation - see if you can locate that episode.

I found the episode - see link below. It was from Holmes on Homes Season 6, EP6067.

Here is a link that might be useful: Holmes: Froundation issues

Is that video available for viewing online? I would like to see it. Thanks!

I recall that video. Very interesting.

However, your house is not falling down. It just looks like one section was exposed to water for too many years and is suffering from deterioration, perhaps from chemicals in the ground water. Sulfate attack, for instance.

The interior parging could be falling off from the exterior-to-interior moisture drive and/or from a wall wetted by a wet foundation drawing in water by capillary action. The outside parging is probably deteriorating from the freeze/thaw cycle. Parging is sometimes applied as a "sacrificial" coating. In any case, you shouldn't expect it to be a permanent covering.

It looks to me like the basement finishing job was designed to hide, not cure any problems. And not done well. The steel frame, for instance, is mounted directly to the damp floor, instead of being set on, at least, a vapour barrier.

Anyway, before you spend a small fortune on hunches and distant guesswork--including mine!--get an inspection by a structural engineer.