Binary Systems contain 2 or more stars that circle each other, and whilst our own star is a singleton, it is estimated that upto 85% of star systems contain more than 1 star.
But, not normally so close together that they are touching !
A Contact Binary set of stars have moved so close together that their atmospheres are now interacting. The important thing to note here is that the actual action in a star, in terms of the fusion, is in the core, so both core’s are independent of each other and fusing the atoms inside, while the outer shell tends to be mostly hydrogen. Gravity from the stars will begin to pull and push matter from one another, with the dominant partner being the one with the greatest mass (not always the largest in size or brightness) slowly winning over time and accumulating matter for itself.
This process can take millions of year, even billions (depending on size and distance, and difference in mass), but the upshot is, one of the stars will be gaining in mass. As the mass increases, so does the pressure inside and so the core will begin to increase and fuse more, bringing the star to an artificially early end. Another mass, and a supernova will occur.
The closest pair so far spotted is KIC 9832227, located in Cygnus and 1843 light years from us and is predicted to merge in 2022.