Demuxing is the process of disabling the dGPU to bypass failing/failed GPU chips. This process is common on the 2011 MacBook Pros with AMD GPUs.
The preferred method is flashing the graphics mux (gmux) FPGA chip with programming that will disable the dGPU. It keeps the GPU powered down to save power, and routes the iGPU to the internal display. The process removes the ability to use an external screen.
DosLabs sells keys to flash the gmux and retain keyboard brightness control. You will need to install a kernel extension on High Sierra. macOS prior to High Sierra works automatically. High Sierra is the newest Apple supported macOS for the 2011 MacBook Pros. Running an unsupported macOS newer than High Sierra can be accomplished with the DosDude patchers or Open Core Legacy Patcher. Both of these options automatically install the kext needed for keyboard brightness control.
The process to flash the gmux is in the DosLabs link above. Afterwards, on High Sierra, follow these instructions. Here is the link to the mirror. The instructions are also included below:
Reboot the machine while holding CMD+R. Once recovery mode is booted open the terminal and enter the following: csrutil disable Reboot the machine. Install the package.