I had some toxic waste (oil, antifreeze, rat poison, insecticide) and being a good citizen, instead of throwing it in the trash to leach into the soil, I drove a half hour to the county recycling center and dropped it off at three different stations.
But what does the county do with it?
In many cases, the oil is used to power some furnace in town. My town uses the waste oil in the DPW garage’s furnace.
Otherwise, they are sent to some larger industrial reprocessor.
Industrial landfills or recyled. Industrial landfills are much more stringent and have more measures in place to protect the environment. Some facilities have special incinerators as well to dispose of the product.
Also they may recycle or reprocess much of the waste themselves, or have contracts with reprocessers. Forex: used lubricating oil is not irretrievably soiled - rather it’s got entrained contaminants in it. There are a number of ways to remove those contaminants safely. (Usually simply passing the waste oil through a lube oil purifier would do the trick.) It may be more economic to use it as a fuel, but it’s not the only option.
Similarly, while it’s prohibitively expensive for a reprocesser to pick up things like NiCd batteries, if they’re concentrated in a central facility, they may become an economic viable source of material.