As recently revealed, chirped dissipative solitons (DSs) generated in a long cavity fiber laser are subject to action of stimulated Raman scattering (SRS). Here we present theoretical and experimental study of the DS formation and evolution in the presence of strong SRS. The results demonstrate that the rising noisy Raman pulse (RP) acts not only as an additional channel of the energy dissipation destroying DS, but on the contrary can support it that results in formation of a complex of the bound DS and RP of comparable energy and duration. In the complex, the DS affords amplification of the RP, whereas the RP stabilizes the DS via temporal-spectral filtering. Stable 25 nJ SRS-driven chirped DS pulses are generated in all-fiber ring laser cavities with lengths of up to 120 m. The DS with duration up to 70 ps can be externally dechirped to <300 fs thus demonstrating the record compression factor.