I had two area's that had stumps 10 years ago. The stumps were gone (Ground down) but there were large root structures just below the surface. When I removed about 4 in of soil, I found the roots. They were soft and springy just to stand on. I found they whent out about 3 ft in several directions. I ended up digging them up and back filling with sand and some paver gravel my neighbor had (He was building a paver patio at the time).

I used a hand tamper and watered it to get it to settle as much as possible. I had to do 2-3 cycles of tamp, water, backfill to get it all solid.