Expeiments carried out on a series of seven different polymers with molecular weights varying over a wide range have allowed us to confirm that stable jets can be obtained at concentrations much below the crossover point. A jet was considered as stable if its lifetime exceeds the Plateau-Rayleigh time by several orders of Magnitude.,The systematic study carried out for polyethylene oxide) solutions in a wide range of high molecular weight showed that the lowest concentration at which a stable fiber can still be formed is scaled by [eta](-2.14 +/- 0.3) or m(-1:63 +/- 1.0.29). However, for the domain of not so high M, the spinnability Concentration corresponds to the onset of entanglements and scales as M-0.70 +/- 0.14 with is the same as the dependence of the crossover concentration On molecular weight. The difference in the scaling exponents reflects two possible regimes of stable fiber formation in fiber spinning. These exponents are close to those obtained by Palangetic et al. [Polymer 2014, 55, 4920] for other polymer solutions in the electrospinning experiments. Several examples of spinnability at very low concentrations for other polymer solutions are demonstrated. A possibility of the formation of stable jets from dilute solutions is explained by an increase of the intermolecular interactions of extended macromolecular chains, resulting in the phase separation and leading to the formation of fibers created by oriented macromolecules. The theoretical considerations show that there are two sources of jet stabilization at low concentrations (high M), namely, the coil-stretch transition and demixing of the polymer solution.