Is it so strange that a sentient creature (presume with me for now that demons would indeed be sentient, for I find it hard to believe they would function otherwise) would choose to deviate from a bloodthirsty nature in order to gain emotional rewards? I thoroughly enjoy thought experiments such as this. There exist species on our planet that coexist in equally "strange" symbioses, for example the Egyptian Crocodile and a small bird called a Plover. Mind you there is a probable lack of affection, more just a beneficial cease fire for the crocodile.
All the same such a relationship between the demon and the mouse mimics the human habit of keeping pets for our own pleasure and their ease of living. Wolves were smart enough to realize some large moderately intelligent apes would take care of them and feed them in exchange for certain affections and labors. What is to say a mouse (or perhaps a rat as they are omnivorous) would not see such a benefit from a kindly demon. After all he only wants and needs to flay humans!
I did not track the time to completion on this one as I was experimenting with a more open and fluid way of working and did not want to pressure myself to finish overly quick.
Process Animation for fun (click the second image to view it).