Whether it's natural subsidence, like sinkholes or human induced subsidence like the collapse of underground engineered chambers or mining subsidence the two ways of dealing with it are backfill or leaving it alone and the enforcement of an exclusion zone.
Where backfill is used for the remediation of subsidence it's generally loose rock fill, because it's the cheapest form of backfill and excavations aren't going to be established against the backfill, particular in civil situations. In mining, the subsidence backfill can be loose rock, sand or tailings, or cemented rock, sand or tailings; depending on circumstance, what materials are available and how much the company is prepared to pay.
Edit: 26 March 2015
I came across this picture of a sinkhole being backfilled with concrete on the MSN news website.
Additional Information 26 March 2015
One group of geotechnical contractors in the US advocates excavation and backfilling of sinkhole where the bedrock in no deeper than 4.5 m (15 ft). For deeper holes it recommends grouting and for very deep holes it recommends cap grouting.
The Karst Sinkhole Treatment document by the Natural Resources Conservation Service recommends establishing of a buffer zone around the hole and backfilling. Depending on circumstances the backfill will include loose rock, concrete and if necessary geotextile.
When floods hit Calgary, in Canada, in June 2013, creating numerous sinkholes, the holes were backfilled.
The Sinkhole Guide recommends backfilling sinkholes with,
“native earth materials or concrete. Broken limestone rip-rap or a
concrete plug in the bottom of the sinkhole often helps create a
stable foundation for the fill. Above that, add clayey sand to form a
barrier that will help to prevent water from seeping downward through
the hole and enlarging it further. Lastly, add sand and top soil, and
landscape to surrounding conditions. Additional fill may be necessary
over time, but most holes eventually stabilize.”
According to the US Department of Transportation, fly ash in grout has been used to backfill sinkhole/subsidence holes in abandoned mines.
In North Dakota, the Public Service Commission backfills subsidence hole in abandoned mines in that State.