For a submanifold $N^k$ to be fiber of a submersion $f: \mathbb{R}^n \to \mathbb{R}^{n-k}$, it is necessary for $N$ to be parallelizable and with trivial normal bundle. If we request $N$ to be just one connected component of a (possibly disconnected) fiber, the $h$-principle applies to provide a complete answer. However, if we ask $N$ to be the whole fiber, then there is no $h$-principle argument. We construct examples of parallelizable, with trivial normal bundle, submanifolds such that they are not fibers of submersions. This is joint work with Daniel Peralta.