Funny you mention this. Most screen readers actually have that as a feature, and it's called screen curtain. As many things in this field, it was pioneered by Apple, but it's available almost everywhere these days.

This opens up really interesting opportunities, think cheating at school for example.

Previously, other tricks have been used to achieve the same effect, including not having a display plugged in at al, Configuring Windows to use a second display while none was actually plugged in, or using a fake HDMI dongle.