Are there any universities that offer free PhD programs?

Only the invisible universities on invisible paper. Sorry. None that I know of. You could look into the online courses. Those should be cheaper but there is nothing free.

I don't know of any free ones, there may be some mills that will print you one for 20 or 30 dollars.
And some church groups that will issue one ( good only to them really) for a fee, but even the dipoma mills will need some fee.

As for as a real program, there are no free programs.

No free rides. You pay through hard efforts even if you do manage to get financial funding.

Are there any universities that offer free PhD programs?
It really depends on the school, program you choose, and what your current job status is. For example, a professor at my university went to USC a well known school, they paid him a certain allowance every year he was in the program. You have to really do your research, and many times your employer will help you financially obtain your degree.

No free rides, but many (most?) PhD students can defray a large part of their cost by teaching undergraduates - being a TA. Depending on the field of study you may also be able to get a grant, typically by doing a thesis on a topic of interest to a foundation or corporation.