A cyst is a closed sac, having a distinct membrane and division on the nearby tissue. It may contain air, fluids, or semi-solid material. A collection of pus is called an abscess not a cyst. Once formed, a cyst could go away on its own or may have to be removed through surgery.
In the following video, a guy squeezes a huge cyst on a mans back and loads of thick tooth paste like pus comes out. So much keeps coming out you think it's never going to end. Unbelievable.
Semi-professional pus removal. HUGE CYST EXTRACTION.