In our world, the reason for extended family, expanded family (non-blood related people adopted into the family) and multiple generations all living together giving way to smaller family units was practicality. A large family group was an asset for the first 10,000 years or so of human civilization after the development of plant and animal domestication and mankind became tied to the land. A big family meant lots of workers for the farm. With the coming of the industrial revolution, this type of family was no longer practical. You needed a small, mobile family so that you could move to the cities where the work was. The ideal unit was the nuclear family. You had a father who could work the factory and a mother who could handle caring for the next generation of workers. And grandma and grandpa went to the old folks' home.
Alvin Toffler coined the term "waves" for describing the various types of human civilizations. The First Wave was the agrarian age. The Second Wave was the industrial age. The Third Wave is what we are now moving into, the parameters of which have not yet been defined. The prominent type of family of a given country will tell you what wave that country is in. If the most practical type of family is the nuclear family, this is an industrial country. If the most practical family is a large extended and expanded family, this is prabably a First Wave agrarian country.
So several generations living under the same roof doesn't necessarily reflect poor economic conditions. In fact, you could say the opposite of a First Wave family. A prosperous First Wave family would have many generations living together, whereas a First Wave family experiencing a year of famine may not have many generations -- or family members -- left at the end of the year.
In short, the line doesn't suggest anything at all to me about Cardassian economic conditions. I wouldn't be too sure, either, about the rise in multi-generational households today being an indication of economic downturn in our own country. We have been leaving the Second Wave and entering a Third Wave, where what was necessary and practical for the Second Wave isn't necessarily so now. The classic nuclear family -- Mom, Dad, and a couple kids -- has been a minority in the United States for many decades now. The nuclear family is on the decline simply because it isn't as essensial as it once was.
The only thing the fact of a Cardassian multi-generational family suggests is that it wasn't essensial that the family be mobile as a family from earth in the early 20th century would need to be.
