It's not for real-time rendering, although the technique in the video Alex_J posted would be perfect if possible in a render engine like v-ray. Having geometry at the intersection who's texture could be blended between the wall and floor texture would be the ideal solution.
there are plently of ways how to tackle this, decals are an option, maybe using vertex masked dirt shader stuff, you could cover the transition with gras, dirt, rubble, rocks meshes etc. maybe it would help seing what you like to achieve in your specific case to help a bit better.