I can help a bit also....
I am sole property POA/healthcare proxy/co-executor on will for my mom who is dying in Florida, while I live in Illinois. Before she went on hospice, I had all her medical bills sent to my address in Illinois, but they were still under her name. So she was/is still the guarantor for her bills, but I pay them using her money that I have access to due to the POA for her regular checking/savings account, and on her revocable trust account. My POA allows me to handle all financial transactions for her regarding personal property, banking matters, insurance matters, etc, but does NOT impose a duty upon me to handle her financial affairs. Meaning if she doesn't pay a bill, it isn't my responsibility to make sure it does get paid(I would, of course, but some people would not, which is why POA should only be given to someone you trust to do the right thing on your behalf).
So what does this mean for your step-mom? If her brother wants her to take over dealing with their mom's medical bills from both a payment perspective, and being able to talk to billing offices/Medicaid, etc, on her behalf, then she will need to become co-agent with her brother on the POA, as well as have HIPAA release forms signed. The POA will allow her to pay bills using her mom's account, and the HIPAA release will allow her to talk to who she needs to talk to, if necessary. As long as she does not make herself the guarantor for any of her mom's bills, she will not be financially liable when her mom dies, and any outstanding bills will be paid from her estate, like Sriram said. POA ends when the person who gave it to you dies, also.
If her brother is not willing to get the POA changed(or provide your step-mom with money to pay the bills), then your step-mom should tell him "tough, you handle the bills/insurance", because otherwise, the only money she can pay them with would be her own.
Then there is the fact that with Medicaid coverage, certain assets that your step-mom's mom may have are subject to Medicaid's Asset Rules, if she does end up in a NH/SNF. End result on that will probably be that her son won't end up with anything once she dies, but that is another story.