Previous work in our laboratory has shown that at very low agarose concentration in water gelation still occurs within mutually disconnected, high concentration regions generated by spinodal demixing. The freely diffusing particles obtained in these conditions are studied in the present work by depolarized dynamic light scattering and probe diffusion experiments. These particles are found to behave as large (in fact, mesoscopic) polymer fibers entangled in a continuously rearranged mesh with scaling parameters typical of partially flexible, neutral chains. The present results allow specifying the notion of mesoscopic gelation. They also reveal that the same symmetry-breaking mechanism that allows macroscopic gelation at polymer concentrations well below the threshold for random cross-link percolation generates additional and unexpected phenomena.