Definitely sosocurious.
One would think: No matter how they are feeling,
or the stage/state they are in, they would want to 'find' their loved one.
Certainly help Police, in every way possible, day or night,
answer/follow whatever Police request.
Answer all their questions, inform them of any 'estranged relatives',
do what ever possible to help find your precious one, to assist in trying to solve the case.
Those closest to relatives have so much information that may help Police.
Don't hide it. Tell them what you think, what you feel.
I guess, if Police, met us Sleuthers, they would say":
"THANKS, join us in this investigation, help us through,
with your inside knowledge of your relative.
Have a coffee, and a 'kit kat' with us".
Perhaps you may be required, to gather further inside info. to assist
ie carry a 'listening device, and don't remove your tracker 'accidentally'.
You would think, they would keep you well informed of the current situation,
knowing you may possess certain knowledge, of the type required in the particular incident.
I know, I would be such a 'helpful pain',
they would leave the country, and enter a different career, to escape my 'help' !!!
When the phone would ring, at the Police station, the answer, would be, "Unavailable.
Sorry. We don't know what country he has escaped to".