Have a mortgage in Greece that no longer can be paid. Been out of work for 6 months. Have a wife and 3 kids and family in North America, that is willing to get us back on our feet.
If we moved to Canada ( have citizenship), can Greece come after us for the mortagage we still owe on the house?
Well, first of all, you need to do what you have to do.
Since Greece is part of the EU there is an approach to insolvency that may be available to you. This is important because if you can hand the house back and close the door on the mortgage debt before you leave Greece then you will not need to worry about the old debt resurfacing.
Greece is an interesting country when it comes to consumer debt problems. As I remember, Austria, France, Denmark and Greece did not allow for the possibility of wage attachments.
Talk to a legal adviser in Greece, for specific responsibilities and rights you may have under the current law. But for the most part, the international debt collections industry is not that sophisticated. I would be surprised if you moved to Canada and anyone chased you or had any legal authority over you for the debt.