'To someone's ...' means creating ... for them. The most common phrases with this structure are 'to someone's cost' and 'to someone's detriment'. For example, of I say I helped you to my cost, it means that helping you created a cost for me. This sentence means that being a burden creates pain (emotional, not physical) for the elderly people.

I agree with Dan. I think this book you are reading was written by a non-native. Probably written by a University Professor that can't speak fluently but can write complex sentences. It is just so unnatural. If it is a textbook for a class in school, then you have to read it, I suppose. But if you like learning English by reading, you should just read websites that are in English and put that textbook away. "to the pain" is just an awkward way to say something is "a pain/uncomfortable about life", in the context of the page you are reading. I hope you survive while reading this book. It is a very difficult book to read. Good luck.

To be honest, it's not very clear here, but I would guess the meaning is: They are a burden on society, and this causes them pain, because they don't want to be a burden on society. Knowing they are a burden, makes them sad. It hurts their feelings. Thus, in this context: to their pain = and this causes them pain = which hurts them

I do not understand this terrible sentence. I cannot even figure out what the subject of the sentence is. The verb is "make", but what makes? It cannot be "burden" because if it were, the verb would be "makes". To whom does "their" refer? To old people? To all the other people listed?