What can I do about 100-year-old stairs that are pulling away from wall
Call the installer, builder or manufacturer for any warranty type of repair...I'm kidding. Your best bet is to get a Carpenter or Stair Builder that uses glues, screws &amp; bolts behind or even upon the finished surfaces...finish screws are wonderful.

Nails, spikes &amp; staples are the norm &amp; they can't &amp; won't last, they're held by friction alone. Glue Coated nails are only good for a decade at the most, glue only lasts if its hold can't flex or break loose. A stair is a moving part, if given the chance, &amp; will only continue to loosen until another object retains it.