Context. Modeling how cold giant planets form around M dwarfs remains a challenge, both because their protoplanetary disks can lack sufficient mass and because such planets are expected to migrate inward while interacting with the disk. Moreover, it remains unknown whether inner rocky planets can survive in systems that host a cold giant around very low-mass stars, which could have important implications for the habitability of rocky worlds. Aims. We investigated the conditions required for the formation of giant planets at large orbital distances (1- 3 au) around a 0.1 M_· star, and explored the circumstances under which a close-in rocky planet can survive. Methods. We performed N-body simulations in which planetary embryos grow through pebble accretion, followed by gas accretion during the disk lifetime. Assuming a local disk turbulent viscosity (α_t) of 10^{- 4}, we included planet-disk interactions throughout the disk evolution, using a new prescription that accounts for the onset of outward migration when the planet-to-star mass ratio (q) exceeds 0.002. Results. We find that a cold giant planet can form around a late M dwarf, even with an initial pebble mass of only 6 M_·, provided the disk gas mass is 10% of the stellar mass. This outcome requires a compact 20 au disk in which the inner, viscosity-dominated region has a high gas surface density set by a low accretion viscosity (α_g=10^{- 4}), that planet- planet collisions assemble a a∼ 5 M_· core within 1 Myr, and that the gas disk survives for 10 Myr. In addition, an inner rocky planet can survive in a close-in orbit if it migrates into the inner disk cavity before the outer body grows into a giant. Conclusions. The initial dust mass required for giant planet formation around very low-mass stars does not need to be as extreme as previously thought. A combination of planet- planet collisions, efficient pebble accretion, and a long disk lifetime plays a key role in enabling the formation of cold giant planets with masses between those of Saturn and Jupiter.