What theory holds that a change in one part of society produces changes in all other parts?

The theory that you described is called the equilibrium theory of social change. It does exactly what you described.

I believe the answer is: equilibrium theory of social change.

According to equilibrium theory of social change, each members of society work as a part of one giant mechanism, so when a certain part of society would not be able to function properly if the other parts fail to fulfil their function.

For example, supermarket would not be able to sell vegetables if the workers of vegetables farms fail to meet their production demand.