Thunderbolt Display Cable
All is not lost if the the main cable breaks
One of the disadvantages of Apple's Thunderbolt display is that the cable is not all stable. This is the main cable from the back of the computer that is used to connect to a MacBook or iMac.
I have seen many Apple Thunderbolt displays encounter a tear in them because of the angle that you have to put it in a MacBook. Over time,
Unlike the power cable, there is no way to take this cable out. The end of the cable is mounted to the mainboard. So if something happens to the connector cable, you can't replace it.
You can see the cable starting to have a tear. It's only a matter of time before it breaks.
Broken but Not Dead
However the display isn't technically dead. You can still use it as an external display. Simply connect another Thunderbolt 2 cable to the port on the back of the display and then connect it to your computer.
The Apple Thunderbolt Display uses the old Thunderbolt 2 connector, not the new Thunderbolt 3 connector - also known as USB-C.
You can find a Thunderbolt 2 display cable on Amazon for about $40. That's kind of expensive for a cable but it is far cheaper than getting a brand new monitor.