We don't know how many years this situation has existed but it hasn't fell in yet. That says a whole lot.
I would consider a footer at the bottom of the 45* with a keyway in it and #4reinforcing rods sticking out every 2' and leaning twoard the angle. Drill holes in the foundation above at 2' intervals corresponding to the lower rods. Stick rods into the upper holes and tie them to the lower rods. Now, place a reinforcing mat of rods on 1' each way. Place 6" of concrete on the 45* slope and pour a floor below. This gives a 'knee wall' to keep the foundation from slipping into the basement and will help to hold it up, vertically at the same time.
You are welcome to contact a structural engineer to verify the plan.