Although many (but not most) of my colleagues receive grants or scholarships, it is common (here) to pay the PhD out of your own pocket. But I do live in Portugal, so factor in the economical (but, mostly, social) context.
The catch is that the student then signs that they will return home for a period (e.g. two years) immediately after the PhD or be liable to pay the scholarship back.
[source: am an ex PhD student, have seen friends under this arrangement].
Yes, there are. I know Cornell(USA) has had such positions. But yes, it is definitely not a norm.
I asked a former university staffer about it once and they told me the money doesn't exist. The university "charges" me x dollars per term, but in my funding there is conveniently an extra x dollars per term in addition to my y salary from the university. So I then tell the university in my funding forms that they owe me x+y dollars and they are like "oh, well we have to deduct x dollars for your tuition". So the net effect is the money doesn't actually exist.
What subjects were these PhDs in by the way?
I am talking specifically about Computer Science. This is not even a modern instance. The first case I've heard about is in 1999.