The effect of charge multiplication in Si p+-n-n+ detectors observed in the unique conditions of the in situ irradiation with 23 GeV proton beam fragmented into 400 ms spills and the temperature of superfluid helium, 1.9 K, was analyzed. The current pulse responses of the detector irradiated to 5 × 1013 p/cm2 demonstrated a two-stage process of charge collection, in which, in the first stage, the current was induced by holes, and in the second, by electrons arising due to avalanche multiplication produced by holes. In the detector irradiated to 2.7 × 1014 p/cm2, the third stage of charge collection was observed that was related to avalanche multiplication produced by electrons reaching the n+ contact and sequential drift of generated holes back to the p+ contact. The developed procedure of data treatment allowed extracting the full set of carrier transport parameters and internal charge gain rising to 3.7 at the bias voltage of 400 V and the fluence of 5 × 1013 p/cm2. An evolution of charge multiplication at the p+ contact initiated by holes originated from a high rate of the hole trap introduction at 1.9 K described by a fivefold rise in the trapping probability at 1.9 K in comparison with its value at T = -10°C. This increases the electric field near the p+ contact and leads to the avalanche multiplication affecting the following stages of charge collection.