For all we know, Tsugumi's house burning down is just an accident that has nothing to do with Kanae's "curse". Somehow Tsugumi picks up on Kanae's self-guilt and takes advantage of her, despite knowing that Kanae is suffering inside. But what does "I stay alive by drinking her spit" mean? And what is the significance of their bird dying?
my guesses: she simply means she stays alive by kissing her - i.e. their relationship is all that is keeping her alive
we see a flurry of feathers on the page before, so i think the implication is that tsugumi killed it, presumably to try to make kanae feel more guilty (the "curse") and bind them closer together