If I remember correctly, Shinigami are "purifying" Hollows with Zanpakuto, cleansing souls and sending them to Soul Society (not counting cases when souls are going to Hell). And regarding Quincy, it was said that the main conflict between Quincies and Shinigami was that, unlike Shinigami, Quincies were destroying souls when killing Hollows, which was bad for balance.
In series, it was shown numerous times that Hollows can also be defeated by humans having certain abilities, for example, Yasutora Sado, Orihime Inoue, Hanakari Jinta, etc. So, what happens with Hollow soul in this case? Is it exorcised, or destroyed, just like by Quincy hand?