In my area we call it multi-generational living.
Over here we call it Whanau, a Maori word meaning extended family. The extended family is very important - brothers and sisters, uncles and aunties, parents and grandparents, grandchildren. It's how I was brought up, and it's how I want my children to live - that they are welcome to come here anytime, and that at some time in the future, I may need to live with them.
When my wife was younger, she lived in the garage at her grandparents place, while her parents put together money for a house, and then built it. For a couple of years we lived in a caravan with 2 young boys in the backyard of the mother in laws place, using a corner of the garage for kitchen and office. Later my 2 daughters arrived with a caravan each. One daughter was back there a few years later, with daughter living in a single room sleepout. Now the sister in law is living in the backyard in a similar sleepout, while the bro in law sleeps in a van. When building our new garage, we put a sleepout on the end for my daughter and granddaughter.
I have no problem with helping out, or being helped...it's what you do for family.