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Wasn't even sure about what the title should be, but I had a thought and I wonder whether it may be possible or not.
Is it possible that there is a star which acts as a mirror and reflects back the light almost as it was received?
My though is that if there is something like that and let's say that the star is far from earth 50 light years, than we could see 100 years back to the past.
I have never heard of any naturally occurring object acting as an optical mirror on a scale large enough to form an image at a distance of light-years, and it seems deeply implausible that anything of the kind would exist. Natural objects are not that smooth or uniform.
Independently of that question though, let's look at how large a mirror you would need. If we assume light with a wavelength of 500 nm, and an optical path 50 light years ($5\times 10^{17}m$) long, and we want to see Earth with $1m$ resolution, we need a resolution of $2\times 10^{-18} radians$ which requires an aperture $2\times 10^{18}$ wavelengths wide, which is just about $10^{12}m$ or about a billion kilometers -- most of the diameter of the orbit of Jupiter.
So even if they were perfectly flat optical mirrors, most stars are simply too small.
See this post about binary stars, which contains relevant information:
Stars are far from perfect blackbodies due to scattering/reflection. This is especially true for hotter stars, because of all the free electrons, but even cooler stars can reflect a significant amount. For example, in aanda.org/articles/aa/pdf/2001/19/aa1009.pdf you will see that they use a reflection albedo of 0.30 for the K star and 1.00 for the F star, but the latter number is not meant to be taken seriously, they simply don't care if the light is reflected or absorbed and re-emitted because it isn't an important term. But the value of 0.30 for the K star might be meant more seriously, though it is still not regarded as a critical parameter because it only affects the color of the light that is reflected, not the total amount of light (given that stars are in radiative equilibrium, so must ultimately return all the incident light, whether it happens by reflection or heating).
Indeed, stellar emissions are often characterized by "effective temperature," to connect the surface flux of a star to the Stefan-Boltzmann formula for the emission of a blackbody by using a T parameter that is not necessarily the actual temperature. When using this notion, as is quite common for dealing with stars, there is no essential difference between heating of and reflection from the surface of the star in question. The details of the difference have to do with the shape of the spectrum, but that shape is generally not a Planck function anyway, so as soon as one is using the "effective temperature" concept one has already parted company from a detailed understanding of the shape of the spectrum. (When you do want the details of the spectrum, you will have to model the situation with some care.)
Is it possible that there is a star which acts as a mirror and reflects back the light almost as it was received?
That depends on what you mean by "as it was received". That post shows that the concept of albedo applies to stars as well; they can be reflective.
