[Vicegrip]

*You can also "puddle" the sand or fine soil into the voids. Fill with sifted fine soil and then flood it with water. you can drive a broom stick deep into the back filled soil and then stuff a hose down the hole. water lubricates the soil and displaces air. the soil will collapse a bit and you can top up the hole. After a while the water will dissipate and the soil will fall yet further.

I might be inclined to ram a steel rod down the holes and open them up then back fill and pack in as much soil then flood the holes and repeat. Deep vertical holes can be ram compacted with a 2X4 and sledge. fill and hammer the 2X4 deep and refill. Repeat until your arms say "Beer!" Once the area is stable for a few months remove 6 inches or so around the landing and replace with good compactable soil. Once water runs through old dirt for a while it tends to render it more porous.

The picture lends me to think the house has been there for a while. If so this is sort of expected as water runs through the walls of the stairwell and washes out the finer particles.

*Old school "fix it yerself" YMMV. got the bux? Go pro and sigh a check.

[BlackTalon]

Definitely would not 'go pro' here myself -- the mudjacking rec was in response to the initial query. Would regrade and make sure water is directed away from top of stairs. Not sure I would put much effort into filling the voids.