Sometimes people want to take a pen display and use it as a pen tablet. There are several options here. In this case, someone doesn't want to see anything on the pen display. It should be blank.
Some pen displays have their power button configured to effect only the screen. You can power off the tablet, which will turn off the screen, but since the tablet is still connected to the computer it will essentially act just like a pen tablet.
Not all pen displays are like this. Many have their power button set to turn off everything. So if you turn the tablet off, you wont be able to see anything on it or use the pen.
If your tablet is connected via an HDMI cable to the computer, you can disconnect the HDMI cable. In every pen display I know of, this will result in a blank screen but the pen can still be used with the tablet.
In your operating system, you can configure the displays settings to not use the screen in the pen display. This should leave you with a pen display that shows nothing and the pen should still work.
Pen tablets have low pointer lag. Pen displays have higher pointer lag. More here: lag
If you use a pen display even if the screen is off, you will still likely see the larger pointer lag.