In my answer to this question, I will talk about the macroeconomy. I will discuss whether the national economy as a whole (as opposed to any one part of the economy) would naturally fix itself if left alone. My own view (this is a subjective question) is that there are factors that prevent the economy from fixing itself.
The main factor that prevents this is the fact that the economy is made up of human beings who do not always act in logical ways. Classical economics assumes that people will act logically and rationally and will have good information about economic conditions. This is not necessarily the case.
According to classical economics, for example, when aggregate demand drops, workers will accept lower wages. They will do so because they will know that price levels are dropping and that the lower wages will still be worth as much in terms of purchasing power as their older, higher wages. This strikes me as unrealistic for at least two reasons. First, workers will not know that price levels are dropping. It is not possible for any one person to know for sure that prices are dropping or to know by how much they are dropping. This can only be determined through massive studies by entities like government agencies. Second, the workers will not necessarily trust their employers. They may feel that the employers are dropping wages simply so that they can get higher profits. Finally, they simply might not like the idea of having their wages drop. It might feel emotionally difficult for them to accept a pay cut.
In the real world, people will not always have perfect information and will not always act rationally. These factors help to make it hard for the economy to fix itself.