Sill plates are the lowest of a building’s horizontal framing members; the vertical framing studs are often fitted directly to the sill plate. Traditionally sill plates were made of wood, but they were susceptible to rotting because of their location. Under older practices, they were installed outside the moisture-protected part of the building. Newer buildings are often constructed over concrete sill plates.
The major issue that can result from using any sill, including one made of concrete, above a stone foundation is dampness entering the crawl space. It's very important that crawl spaces be kept dry. Cold, wet air sinks, so it has a tendency to enter crawl spaces. While solid concrete foundations are relatively watertight, stone foundations -- those made using recycled building materials, often called rubble -- are notoriously permeable. It's therefore desirable to install a vapor barrier that covers the stone foundation and runs up the insides of the crawl space void to reach the sill plate.
In a departure from traditional construction practice, some professionals don't seal the crawl space from the occupied space with a vapor barrier and insulation. Rather, they prefer to treat the crawl space as part of the building, sealing instead the top of the foundation. It's believed that this reduces condensation on the undersides of the floors of the occupied space, in turn reducing moisture levels inside the building. In older buildings without vapor barriers, or where the existing barriers are compromised by age, retrofitting can be performed using the same layout. Consult with the local code enforcement office to confirm no regulations would be contravened by this configuration.
With stone foundations it's common to find that the top surface is too uneven for a vapor barrier to be held in place by horizontal batons. Gluing the vapor barrier is entirely possible. First create a reasonably dust-free surface on the rubble so the adhesive can find a solid purchase; rough wire-brushing is usually sufficient. Using the polyurethane-based adhesives available in tubes from home improvement warehouses normally results in a good, firm bond. The same adhesives bond polythene to block piers, and polythene to polythene, if strips of vapor barrier are being used, rather than sheets.