Not sure what your question is? Do you mean stop losing soil? You could turf it in the spring, which will stop the soil moving when it roots, If its very steep you may have to peg the turfs and is it too steep/unsafe to mow? You could look at covering/pegging it with a weed suppressant membrane and planting with low maintenance ground cover plants the membrane will help keep the soil in place till the plants take over. One other solution is to terrace it.

This question reminded me immediately of the bunkers on the local Carnoustie Championship golf course! I was intrigued to see how they grow the grass on the almost vertical edge of the bunkers. They cut very narrow strips of turf and then pin them in one above the other. this is in very sandy loose soil and it seems to work well. Hope this helps!

A method used by local authority road engineers is to hydro-sow the grass. A contractor comes in and sprays a mixture of grass seed, fertiliser and some sort of adhesive 'stuff' ontop the steep banks and the grass takes very quickly. As far as I know, this is not a task for the DIY gardener.