In this paper we performed the experimental and numerical study of a passively mode-locked fiber laser that generates packets of sub-picosecond pulses instead of individual pulses. The proposed configuration is a figure-eight fiber laser scheme, which includes a Nonlinear Optical Loop Mirror with polarization asymmetry inserted into a ring cavity. No experimental evidence of self-starting mode locking operation of the laser was observed; however, for proper adjustments of the wave retarders included in the setup, a mechanical stimulation triggers the onset of mode locking. The autocorrelation of the generated pulses shows a narrow sub-picosecond peak riding a large sub-nanosecond pedestal whose intensity is half that of the peak, and the optical spectrum is smooth and wide. We show that contrary to conventional ultrashort pulses, these pulses do not vanish rapidly after propagation through a long dispersive fiber, which makes then attractive for super-continuum generation as well as for applications in metrology. Finally, we study the pulse formation in the laser and present arguments based on experimental data and numerical simulations that the observed pulses are actually sets of a large number of solitons.