It's not quite that simple.
In most cases, the person tends to build a tolerance to the pain, as well as their pain medication. This causes what is known as "breakthrough" pain episodes, which can be much more painful than their usual chronic pain levels. These pain episodes can also last for long periods of time and happen several times a day. They are usually unresponsive to pain medications.
However, in some cases, the person may build a tolerance to their medications and not the pain. This can make it seem like the pain is getting worse when really the pain medications are no longer working effectively.
In rare cases, the person may have developed a tolerance to their pain, but their pain has gotten dramatically worse because their injury or disease has progressed requiring them to take more and more pain medication. This, in turn, can cause them to develop a tolerance to their pain medication resulting in a vicious cycle of chronic pain that is not helped by medication and is getting progressively worse.
Treating chronic pain is an art form, and because of recent changes to opiate prescribing limitations, it is becoming more and more difficult for doctors to be able to manage their patients' pain.