Engineering of new refuse sites is pretty well understood and sophisticated these days, at least in most advanced economies. The bottom of the site is sealed with a multi-layer impermeable barrier, and any effluent 'liquor' flows down to a drain where it is tapped off for processing. Methane and other gaseous build-ups are vented through pipes at the top of the site.

Subsidence due to settlement of refuse over time is dealt with by well-known construction techniques for less-stable ground, such as deep piling. In some cases though it's simply more sensible to repurpose the land for amenity use, where subsidence is less of a concern than it would be for a residential area.