Nice reading.
I also didn't understand why Leiki said that would fuck Helen if she had the strength. [/spoiler]
The way I took it is that Leiki was just extremely grateful to have company and for being allowed to stay.
I'm not 100% sure I understand the story completely, but I can say that about a lot of stories that I read. My interpretation is that Leiki is the monster. Now exactly what the monster is, I can's say. I think it only manifests when Leiki grows extremely hungry. Until that point Leiki thinks she is a normal human. I also assume that their is some sort of physical transformation since Leiki seems to lose a lot of jackets. At the end, Helen, consumed by hunger but still maintaining her own personality, goes prepares to go outside to check on the "monster" but quickly succumbs to her bloodlust. She transforms into the real monster, slaughters Helen, and then goes outside and kills the bear, losing her coat in the process. She leaves Helen's home, the memory of what she really is slowly slipping away, and moves on to find a new house...and victim.
I could be completely wrong about all of that.
One thing that points to my theory being incorrect is that Leiki remembers how many coats she has lost a the beginning of the story. Secondly, if she loses her coat in a physical transformation, I'm not sure how the bear got a hold of it. Well, now I'm more confused than when I first started to try to explain it to you!
p.s. Is there any significance to the protagonists name being "Leiki"?