Gap between pre-cast stairs and building

A long time ago some precast concrete stairs were put in place up against a concrete area (band) of the brick building. The filler material has given way, and there's a 1 to 2-1/2 in gap between the steps and the building. The only bridging material anyone can recall was a hunk of pipe insulation wedged in there and covered with an inch or so of patching concrete(!). You can go under the stairs to a basement apartment, so just brute-force filling the crack with concrete up against a joint filler won't work unless there's a way to keep everything from just falling through. The underside of the stairs has a corrugated look (big corrugations: 3 in wide (or so) recesses and protrusioons that extend a few inches), and the side next to the building is the last recessed area, so there's a depth of just about 3-4" from the top of the top step, to the bottom of the underside here. My thought was to glue a 3/4" joint filler to the building, make a long, thin, shallow trough out of something like hardware cloth and put it between the filler and the stairs, and fill that with an anchoring cement.
Without being physically anchored, I expect this to eventually slide out, just as the last repair did, but it might last longer. Might not.
Any other suggestions?
Thanks in advance.
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snipped-for-privacy@hotmail.com wrote:

if its not structural just cover with a wood or other item TRIM and paint whatever color you prefer.
such dissimiliar items will always move around, trim letys it move without causing grief
attach trim to either building OR steps but NOT BOTH! soi stuff can moive
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