Stars expand after they leave the Main Sequence and ascend the giant branch of the HR diagram. The change is size is large. A one solar mass star can become as large as 100 times its main sequence radius.
In this example, the two stars are originally be quite small compared to their separation.
One star evolves off the Main Sequence, becoming much larger. Its outer layers move towards the other star.
At some point, the outer layers of the expanding star overfill its Roche lobe and become more gravitationally pulled toward the companion. In this way, mass may be transferred from one star to the other.
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