You Ask How Much I Love My Cat
In her dotage, Old Cat wants to nap on the stairs, possibly to keep track of where I am (usually upstairs) and where my husband is (usually downstairs) at a given time. She chose the darkest spot, where the upstairs light doesn't reach. (The downstairs light isn't left on because it's a chandelier and therefore terribly inefficient--though workable for avoiding cat traps.
There are two possibilities for terror:
First, one of us might trip over her and hurtle to our death.
Second, one of us might kick her and injure her old, brittle bones.
She doesn't seem to care, though I have explained the perils to her very patiently, several times.
Hence the lamp. It lights that central area just enough that we can see her there, and she actually seems to enjoy its little glow.
She doesn't have to sleep on the stairway. She already owns the couch, our bed during the daylight hours (and a large share of it an night), the ledge on the kitchen window, and several unknown places where she hides when company visits or the dreaded vacuum cleaner appears. Hubby has shooed her off the stairs several times, because (silly man) he thinks she'll learn not to settle there. I recognize that she's decided she LIKES that step, and by George, she's going to have it.
Again, the only sane solution is to give in to her and arrange something to prevent disaster, like give her a little furniture in her new abode.
What we do for our beloved pets!