I suppose that you are asking about a reality where our solar system contains 2 stars if so, here are some answers I thought of
The Sun engulfs the other star In a couple million years
- this would happen if the second star is considerably smaller than the sun. For example, a white dwarf. It would increase its temperature of the Solar System slightly, but will not have much effects on planets.
There comes a black hole (rare)
- If the second star is extremely large like EXTREMELY large, large enough to collapse under its own mass when combined with the mass of the Sun, then the joint star would end up as a black hole, and would probably swallow the inner planets.
The stars will coexist in harmony
- This would happen if the size diffrence between the two stars is not very large, and they could find a harmonious barycentre (Their centre mass) to orbit. These are called Binary Star Systems. Almost one third of all Solar System in the Milky Way are Binary.