See question above. Since they gave up on finding their dear one alive, should they still spend effort and money to find the body for proper burial?

As mentioned in last question, Halacha dictates that even if a person drowns in a lake or other contained body of water, the family does not begin Shiva and Kaddish recitation until they find the body, or they believe the relative drowned and they give up the search. Shulchan Aruch, (Y. D. 375: 7), Yerushalmi (Shabbos 19b), Pirkei D’Rabi Eliezer (39) and other Poskim rule that interment in water is not considered burial.