I answered the poll with an emphatic yes. That is what my family does. When my grandfather died, my sister moved in with my grandmother. Their house was just up the street from my sister's college so it worked well for them both. She lived there for 6 years until moving out to share an apartment with a friend. Then my brother moved in for a year. My cousin tried it but only lasted a few months. (She didn't win any prizes for that.) Then my mom took over.
I stayed to live with my parents when my mom got sick with cancer. Now I look after my dad. I've worked in nursing homes before and swore I wouldn't let my my family go to one if it was humanly possible to prevent it. They aren't fun places. Assisted Living homes can be better but nursing homes are places people go as a last resort. They tend to be depressing and people get forgotten.
But before you go into the role of companion/caretaker just be aware what you're getting yourself in for. The trouble living with someone with dementia is that they become disoriented easily. You need to be mindful they don't leave the stove on or walk outside in the middle of the night. My aunt cared for an elderly relative with dementia for years. They traveled with her but needed to setup various methods of watching out for her. Blocking the door with the suitcase stand, putting bells on doors, closing off the kitchen at night, etc.
The good thing about being young and living with an elderly relative is that you do gain from their experience. It made a great stepping stone for my sister moving from home to our grandmother's.
If you think you may not have what it takes and will flake out in a few months then save your aunt the disappointment and back out now. When my cousin ditched on my grandmother it left our family in a crisis mode while we made alternate plans. There's nothing worse than relying on someone only to have them flake when you neet them.
If you can't make the committment full time then maybe you can be a temporary relief sitter for your aunt. She can move near your sister for the regular backup care/socialization (old folks get a huge boost visiting with youngsters) and you can visit for weekends or middle of the week breaks as your schedule permits.
She doesn't need major financial help... she wants family to be around, to keep my g'mother company. We all lived practically together until I graduated high school. And she wants to try to provide that again for my g'mother. The rest of the family understands that it will not be the same as it was before, and i think that'll be the hardest part on her.
At this point, I really don't know what I'm going to do. I just want to know I'm not trying for something outragously crazy.
If your aunt is hoping to provide family closeness then she may be better off moving to where the largest amount of family currently resides. She's hoping for more distraction/attention for your grandmother. That suggest to me being near your sister and great grandkids is better.
It's really up to your decision on what you think you're capable of giving. Like I said before, giving time to family is something I'd do in a heartbeat but I also have the scars to remind me when things got hard.