I quit today and a lady from HR emailed me to ask if I would be staying in the country after my last day with the company. I fail to see why they need that information.
( 6 months ago )
Yes, in general you should provide a contact address.
It depends on the laws of each country, but in most cases there are always important documents, the last pay check, references (and more like these, you get the idea...) that can only be produced (and mailed to you) after you leave.