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Stars do sometimes combine (stellar merger), sometimes merely from two single stars colliding, but this is infrequent ("Space is big. Really big...") and undoubtedly most combining stars either are binary companions or include a binary-star member. Binary stars can undergo appreciable orbital decay (from tidal effects and from gravitational waves) to the point that there is mass transfer, which under some circumstances increases the decay, potentially leading to merger. Many stars eventually expand (giant stars) large enough to make such mass transfer between binary companions more likely. Also, they may develop a common envelope, which is minimally a temporary merger, but though the individual stars might survive the common envelope, it causes or increases orbital decay and the stellar cores may merge before the envelope shrinks, so only single body remains. Also, when a third star passes close to a binary star, the three-way interaction is likely to result in a binary with smaller orbit and undoubtedly in some cases the interaction includes a collision. Globular clusters and similar high-density groups of stars provide the most opportunity for this.
Any mass transfer causes changes in stars that make them different that what is expected of a single star (peculiar star) and stars that result from a complete merger add additional possibilities. Models of the history of such stars are of interest and have successfully matched observation, but the variety of outcomes would seem to be endless.
One model of Type Ia supernovae is they can result from collisions of white dwarfs, most likely from a decaying orbit. GW detections are ascribed to the collision and merger of stellar remnants following orbital decay, as are short gamma-ray bursts. Various types of collisions and mergers of stars and/or stellar remnants have been theorized as the cause of some other types of transients.