If by "free," you mean many PhD programs will waive tuition for grad students, then yes. You might also be forgiven for thinking that you actually make money as a grad student because you're getting a small stipend (depending on the program anywhere from ~20k-33k to start).

That being said, they get far more value than that back from you and then a pound of flesh for good measure. You're only taking classes for 1.5 to 2 years, and then the rest of the time you're doing research for your advisor, teaching courses for them, or doing their grading for them. Don't get me wrong, you get a lot back in return in terms of knowledge, experience, and the degree. There are many great mentors who don't abuse the system and do their best to graduate you in a timely manner, but even in those best case you're still on subsistence wages and some programs explicitly forbid outside employment or income.

Only for undergraduates who qualify for financial aid support.