If you have a broken door, especially a crack in the pane, the following information will help to relieve your concerns.
If the glass is damaged below approximately waist height then it has to be toughened to the British Standard. This can be achieved by heat treatment to toughen the glass, laminated glass or adding an approved plastic safety film onto the glass. Either way it must meet building regulations.
The red area is critical location and needs to be replaced:
The regulations were implemented based on risk analysis of the hazards and possible injuries from glass at vulnerable locations.
A swinging sheet of glass (whether in a door or window) is more likely to sustain damage and more likely to cause injury if damaged, than a fixed, or limited opening Casement Window.