Is there any chance of survival/recovery chances for someone with a stage iv cancer?

These are different: Patients can recover from stage IV cancer with appropriate treatment, but they still will not survive.

With some cancers: While most cancers that have advanced to be called stage four are not survivable ever disease site, meaning where the cancer arose from, has different behaviors. For instance head and neck cancer can easily become stage four when it involves multiple lymph nodes in the neck. However, this is very common and we know that even those stage four head and neck cancers have a fairly high cure rate.