She's not going mad - that ship sailed a long time ago. Bellatrix is confused about Sirius and his untimely death at her hands.
Sirius has plenty of his own problems to worry about, but he's never seen Bellatrix cry before... Bellatrix/Sirius friendship.
Just because it shouldn't happen doesn't mean it won't. Perhaps it already has. Remus/Sirius, mild slash.