Some carpenter years ago thought that two nails would be enough to hold the stairs up. They did, for a decade or two, but they would eventually fail when the stringer began to split around the nails.
The stairs did not collapse, no one was hurt. On the other hand they had sunk about an inch and felt decidedly unstable underfoot. Another weekend project!
Remove the old nails to free everything up. Use the 3.5 ton floor jack to push the stairs back into place. An aluminum plate and wood glue to splice together the split stringer. Quite a few new bolts, not nails, to hold everything together. A bit of 3/8″ threaded rod on the other stringer to secure it to a joist. I think everything is secure, solid underfoot again. I just need a little paint to cover over the new work.