Veteran's Links
Jeff thinks their predicament and happenstance usefulness to each other is profoundly hilarious, and at first tags along for no real reason whatsoever beyond staving off the other monsters because he can. As he learns more about Eliza, he realizes just how miserable her own situation is, and believes it's only fitting that she be the one to finally end his life -- for good, this time.
Jeff is another monster, but the ones chasing her are afraid of him, so she needs him around. Jeff certainly succeeds in coming off as heinous and careless but his bluntness also leads her to see he was- is- human and something happened to him. He's unhappy and she can't believe that his situation is own choice. He just won't listen to her and that it makes harder for her to redeem herself for abandoning her friend.