Enneagram Stereotype - Type 4's are Depressed
It may be true that most, if not all, type 4's have been depressed at sometime in their life. That may also be true of many Enneagram types. With type 4, depression, sadness or melancholy can arise as a byproduct of other processes or triggers.
Envy as the passion or sin for Enneatype 4 can often be a trigger to a sense of hopelessness. It's not so much that the individual truly desires what another has as it may be that what the other is or has reminds the type 4 of their sense of deficiency. This hopelessness or sense of deficiency may take on a variety of forms (e.g., not fitting in or being accepted into a particular group or culture, unable to achieve a certain level of competency or status, etc.).
One way to look at it is in terms of an oscillation between two different self-images - the ideal and the despised. The ideal self-image is imbued with all the positive potential of what one could be. The despised self-image contrasts the ideal by highlighting all the negative self characteristcs. Hopelessness can spring when envy, frustration or some other trigger reminds type 4 of the unattainability of the ideal self-image. When the ideal is seen as unattainable, the despised or defective self-image may jump to the foreground.
A sense of defect may trigger feelings of unlovability, incompetency or in general a sense of separation. It's the sense of missing connection that can trigger a search in type 4 to seek out what's missing. The imagination offers felt possibilities of what's missing while reality always seems to fall short. What can be imagined can be made perfect, what is real has to be accepted with all its imperfections. Feelings are checked for whether the perfect connection is made. From a distance, the imperfections can't be seen and the feelings indicate a possible connection. Up close, the imperfections appear and the feeling of connection wanes.