Are unpaid postdoc positions common?
What the group leader should have said is that s/he has no money, but you can join the lab if you have your own funding (i.e., a fellowship). For them to dangle papers in exchange for free work is unethical and potentially illegal, depending on where they are.

Edit: What follows is entirely my personal opinion. I am no lawyer so no idea about legality; feel free to let me know if you think my opinion is too harsh/wrong.

Any kind of free labour in a lab is unfair and discriminatory. It locks out those in society who aren't lucky enough to be able to give their time away for free. This includes undergraduate internships. If you're working for someone, then you should be paid for your time. Even if you are receiving training.