" Mind Manipulation, Corruption, Madness Manipulation (Type 2, Can exist within Astral Chaos for an extended period of time without being corrupted or driven mad) and Soul Manipulation (His soul was strong enough not to be denied its existence from Astral Chaos). "
This feat was done during his Soul Chronicle where he was sent to Astral Chaos and went to and from the Soul Calibur Universe due to it. Astral Chaos corrupts and drives mad those who enter it and weaker souls are denied the right to exist.
The Madness and Corruption effect is proven by not only Cassandra, but the Malfested who are in Astral Chaos. It is also the fact that Astral Chaos is filled with Soul Edge's power which drives others mad and turns them malfested, see the Evil Seed and what happened to Kilik as well as the monks in his temple.
As for the weaker souls being denied the right to exist.