It is, generally speaking not part of the folded cascode configuration. The use of the extra transistor is defined by the application it is used in. It has to do with the input CM voltage. For example, if Vb is higher than the input common-mode, the extra transistor will steal more current from the tail current source. So, less current will be subtracted from the output PMOS current sources by the input diff. pair and the output will go up. Thus, at the output you have information about what is happening to the input CM voltage. A feedback can be wrapped around to control the input common mode.