Captive Sunset

Imagine the Earth slows and stops its normal 24 hour spin but remains tidally locked to the sun. The only safe place for life is where the Sun sits just above the horizon, either dusk or dawn. The Goldilocks zone where it doesn't get too hot or too cold. Our hero is there and tryng to survive as the world he knew begins to vanish. He wondered about the no spin at all possibility or if the Earth became tidally locked with the Sun, one side would always face it while another would never see it. This could send the dark side of Earth into a frozen tundra, while blazing the light side into a furnace.On the other hand it could also follow a path where one complete rotation around the Sun (one year) would equate to all sides sharing the time facing it.