When we talk about economic instability, we are talking about a situation in which people do not know what their economic fate is likely to be. This is not simply a time when the economy is bad. Instead, it is a time when the economy is unpredictable. The main social consequences of such a time have to do with the fact that people face uncertainty in their lives.
When people face a great deal of uncertainty, society suffers. Most of the things that we do that are productive and helpful to society are things that we do because we have some degree of certainty. We have children when we feel certain that we will be able to support them. We pay for college when we are certain that there are jobs that make going to college worth it. We buy houses when we feel certain that we will keep our jobs long enough to pay for those houses.
When there is uncertainty, all of these things become less likely. This harms society. When people do not feel confident enough to marry and have children, the forces that tie society together get weaker. When people do not feel confident enough to own their own homes, neighborhoods suffer. In short, when people face economic uncertainty, society becomes weaker because people are less certain of what will happen to them and are less willing to act in ways that will improve their society and make it stronger and more cohesive.