It's generally accepted that you can't use passive optics to focus light from one black body onto another back body and create a spot hotter than the source. Otherwise you could put a heat engine between the hot and cold spot and generate work. https://what-if.xkcd.com/145/
But imagine taking your bathroom mirror out into space somewhere near the sun, and some of the light gets radiated back, would not the patch of sun directly bellow the mirror get a bit hotter due to incoming light from the mirror? Is this a different problem because normally it is more than one body? I could still imagine some kind of machine connecting two patches of the single body and generating work, I think it is problematic.
While thinking about this I was reminded about sunspots, and I think I've read somewhere that from the outside they appear a little colder than the rest of the surface of the sun, because the magnetic fields somehow trap that heat, and in theory there is a hotter region bellow, which if you think about it is pretty similar to putting a mirror out there.