Is unresponsiveness a common problem in the end stages of Parkinson's disease?

Yes. Unfortunately, people with Parkinson's often go from ambulatory and verile to bed-bound and senile in the end stages. Many medications can delay this progression, but once it gets to that point, hospice is a great option for care.
Yes. Parkinson's disease is a neurodegenerative disorder. Patients become less responsive over time with rigidity, slowness of movement and dementia, among other symptoms.