In germany(*) (and I would guess all over the world) there are no special laws for people vanishing in any science fiction/movie style. The general laws about missing persons would apply.
Without any body or other evidence to prove a person is dead, they are not dead in the eyes of the law.
To be missing and later declared dead legally, you have to be "verschollen" first. This is what "Verschollenheitsgesetz (VerschG)" is about.
Verschollen ist, wessen Aufenthalt während längerer Zeit unbekannt ist, ohne daß Nachrichten darüber vorliegen, ob er in dieser Zeit noch gelebt hat oder gestorben ist, sofern nach den Umständen hierdurch ernstliche Zweifel an seinem Fortleben begründet werden.
A missing person is one whose whereabouts are unknown for a long period of time without any information as to whether he or she was still alive or died during that time, provided that the circumstances give rise to serious doubts as to his or her survival.
A person that is considered "verschollen" can be pronounced dead by a court. This is only possible after 10 years of being "verschollen", 5 years if the person was 80 or older and cannot be done at all if the person is not at least 25.
It is not enough that the missing person did not communicate. For example you cannot have someone pronounced dead, just because they left the country and did not contact you for years. There has to be some indication that they may indeed be dead or at least your good faith efforts to find them where not successful.
There are also shorter periods for special cases: People that went missing during a war can be pronounced dead a year after peace, a person lost at sea in a shipwreck after 6 months, a person missing in a plane crash after three months. All these factors make it more likely the person is actually dead.
So by those laws, there will be no shortage of work for judges 10 years after the event.
Now, if I had to speculate, I would say that there would be a specific rule for this global event, not unlike the exceptions listed before. But that is just as much science fiction as the example.
(*) This should be very similar in austria, since the laws quoted above are originally from 1939, when Germany had annexed Austria. Later after the liberation, both countries kept them. Probably under slightly different names, but generally they should still work very similar.