I would say its up to the fiction. The player of the dead character may take on the walking dead compendium class for instance, in which case the player is still involved with that bond. Perhaps the player likes to make a new character that is similar to the deceased - a friend, sibling or competitive rival - thus taking on the bonds from the dead character. If the bond involves more than one NPC, perhaps it 'morphs' into a newer, more focused bond on the third party involved
If there is no connection, well then I'd say that the bonds are unresolved but the player has the option of taking on new bonds to replace the defunct ones.