I dug a bit. The legal ground of charging families of victim is this: When a person dies, his legal heir inherits all the rights and duties associated to his property (NOT his property itself. Civil Code, article 896.) The company asks damages from the deceased's property, which is a duty to be fulfilled by whoever inherited the property. In case the family members declared to abandon inheritance when the victim deceased, however, they are not liable.
https://www.reddit.com/r/todayilearned/comments/1khj2n/til_i...
So I can definitely see how this makes perfect sense when it comes to doing "damage" to apartments (even if only due to reputation / superstition) if there are direct guarantors, but as the news about JR show there must be something deeper going on here.