

You mean a tide locked planet, as in, one side of the planet would always face the star? The Moon does this with respect to the Earth, so yes, it is possible.
If you mean no spinning around the star, then no. The orbital equilibrium is given by the attraction force between the planet and the star being countered by the centrifugal force of the planet spinning around the sun. If the planet were to slow down, it would move closer to the star. If it would stop, it would eventually fall into the star.





Maybe there should be quality criteria for what constitutes an idea worth discussing. Not every social media post is an idea.