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
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.