The graduate school limits are higher, but still exist. Med school students, for example, simply cannot fund their entire education through federal loans. The maximum period you can get through federal loans in any circumstance is around $140K, and medical school almost universally costs more than that.
https://studentaid.ed.gov/sa/types/loans/plus#how-much
It is possible to discharge student loans (not just Plus loans) in bankruptcy, but you have to basically prove that you can't survive while still making the payments. I don't know if it is easier to discharge the Plus loans or if they all require the same level of hardship.
The parent can, of course, take out unlimited amounts of money if their credit qualifies them to, just like they could by going to the bank themselves and asking for a loan.
As far as I can tell, a combination of different loan programs the government will loan any amount of money toward the cost of college with the only "limit" being for undergraduates. Your parents have to take out the loan for an amount in excess of the $12.5k to $18k yearly undergraduate limit. Once you get to grad school you can borrow the entire amount directly. Once you get to the Plus loan program (which doesn't appear to have any limit) there is a credit check required.
There used to be a private loan program (FFEL) where the government would guarantee the loan amount, but I think that was shut down in 2010. I'm sure you can also go to a bank and just get a loan directly, but I don't know what type of special rules apply to those.