I would say they care about a potential Husband's personality. So likes and dislikes are factored in when they choose a mate. It is also specified that a Mamono will not marry someone who is not compatible with them. They can sense who would find them attractive, or what interests align with their own. So a man would not end up with a woman he did not or could not love.
As for unhealthy or bad relationships, again Mamono are not abusive. Even the more dominant kinds such as the Ogre or the Dark Elf deeply care for their Husband, and would never do anything to hurt him. (In the case of the Dark Elf they only search out men who possess a concious or unconcious fetish for BDSM and submission. So not abusive just hard dominant behavior.) It has also been noted that a Mamono woman will take a man away from a Human woman if the woman is abusing him and care for him instead.
All in all the Mamono possess a sense of morality and a protective nature though it differs from what many might consider to be moral.
Hope this helps.
Cheers,
The Weary TimeLord.