In the context of tidally locked planets orbiting M-dwarfs within the HZ, what could allow life to thrive around the terminator line?
Answer
A sufficiently thick atmosphere could circulate heat from the perpetual dayside to the nightside.
Even if tidally locked, a thick atmosphere can distribute heat absorbed on the dayside around the planet, potentially creating a stable temperate band around the twilight line (terminator) where liquid water could persist.

#Videos
What Is the Habitable Zone? - YouTube
Related Questions
What familiar analogy is commonly used to describe the Habitable Zone?What primary role does liquid water play that makes its presence essential for life as currently understood?What results when a planet orbits too close to its star, as believed to have happened to Venus?What mechanism might maintain liquid water oceans subsurface on worlds like Europa or Enceladus, far outside the traditional Habitable Zone?The placement and width of the Habitable Zone are primarily dictated by what stellar characteristics?How does the Habitable Zone for a dim, cool red dwarf star compare to the Sun's HZ?What effect does a planet's orbital eccentricity have on its potential habitability within the HZ?What is the essential role of a planet's atmosphere in modifying conditions relative to the calculated HZ?What is the primary function of a strong magnetosphere generated by a planet's core?Why are geological processes like plate tectonics considered vital for long-term habitability, even for a planet perfectly situated in the HZ?How does the Optimistic Habitable Zone differ from the Conservative Habitable Zone?In the context of tidally locked planets orbiting M-dwarfs within the HZ, what could allow life to thrive around the terminator line?