The stabilization problem in control theory is the following: given an unstable plant, find a controller, such that the overall transfer function of their feedback interconnection is stable. It is known that plants possessing a coprime factorization are stabilizable. This raises the natural question in the title. It is also known that if the ring of stable transfer functions under consideration is projective free, then the answer to the question is yes. In this talk we will show that common classes of stable transfer functions are indeed projective free. (This is joint work with Alexander Brudnyi from the University of Calgary, Canada.)