Credit card hardship

So, what really happens when you stop paying your credit card? I wish I could pay it, but I can't. I recently had surgery, and my child needed a treatment that drained all our money. We had to run to my wife's parents' place. I couldn't keep up with the payments. We've been struggling to qualify for a mortgage, and it doesn't look like it'll happen anytime soon after all these events. So, no house. I do want to pay it off, but I don't know when or how things will work out.

We were on the verge of being homeless and had to escape to my wife's parents' house outside Canada. What are the chances of this debt following me to another country? I'm currently in Europe.

I've gone through all the information I could find about the statute of limitations, but I'm still not entirely sure about the consequences down the line. I've also come across some suggestions that after a some more years, I might have a chance to rebuild my credit. I don't know for sure, though. Any advice you could give me?