Red dwarfs
Claim in the list: Red dwarfs are the most common type of stars and can shine for trillions of years.
Verification: Supported as an approximate astrophysical conclusion. Red dwarfs (M-type stars) are the most numerous stars in the Milky Way. Because of their low mass and slow hydrogen consumption, models predict lifetimes of up to roughly 10–14 trillion years for the smallest red dwarfs. This is a theoretical lifetime; the universe is only about 13.8 billion years old, so no red dwarf has completed its full life cycle.
Conclusion: Red dwarfs are the most common stars in our galaxy, and the smallest may shine for trillions of years according to stellar-evolution models.