Rather than a standard "groundcover", I'd look at any lowgrowing, spreading perennial like candytuft (Iberis sempervirens), rockcress (Arabis species), basket of gold (Aurinia saxatilis), sunrose (Helianthemum nummularia), snow in summer (Cerastium tomentosum), creeping phlox or Lithodora diffusa.

All of these are more or less evergreen and offer a showy bloom period. They only need a quick shearing back after flowering to keep tidy and groomed looking. But they will not drape endlessly - you can only expect a foot or two drape over the wall at most.

Some dianthus varieties drape well. "Pinks" seem to stick in my head.

Martha

You might consider prairie winecups (Callirhoe involucrata) or woolly speedwell (Veronica pectinata).

I would like to second candytuft, Dianthus 'Bath's Pink', and rockress. Would also like to add Sedum 'Angelina' and 'Blue Spruce'