What is typically done when a voice actor for an ongoing series passes away?
A similar thing happened with Tomoko Kawakami, who voiced Soi Fong while Bleach was still airing.  While she went on hiatus due to ovarian cancer, she was replaced by Houko Kuwashima.  Once the news of her death broke, Kuwashima assumed the role until the end of the series.

It's a sad day when a seiyuu passes, but the general trend has often been to keep the production going.  Characters are seldom written out of the anime if they are based on an existing media (Bleach, One Piece, etc), so anything that would involve the character not showing up during critical, canonical pieces of content wouldn't be feasible.

The only times I've heard of series being cancelled is when a major player, such as the mangaka, passes away.  This was done in the case of Kaze no Stigma, as Takahiro Yamato had passed away, leaving the series incomplete.