This was actually the perfect series to follow up Welcome to the NHK with, as both series deal with subjects that terrify me, but approach them in a surprisingly soothing way. For NHK, it was the subject of future and searching for a fulfilling life, and for Haibane Renmei it was death, and...also searching for a fulfilling life! They're both radically different series with radically different approaches to their subject matter (I don't think anyone can doubt that Haibane is far and away the more soothing of the two), and both ended up working for me.
Haibane Renmei's approach to death itself is interesting in what it explains and leaves open, but it's made even more interesting by the lesson that's learned from it, because it's not confined to death; it's all about learning how to let go of someone you love when they wish to move on, the pain associated with it, and the joy that can come out of it. The story really is more of a lesson of empathy, understanding, and growing up than anything, and it executes it admirably in a way that's neither too idealistic nor utterly bleak.
The ending is beautiful and one of the best conclusions to a series I've ever seen. It doesn't tie all the loose and ambiguous ends its worldbuilding left, but it doesn't really need to.