Closing terminal window dosn't kill sudo'ed program

[Ralf Mardorf]

PS:
Now I understand the problem in our communication.

It depends on the way you set up sudo.

Assumed the OP does use sudo asking for a password, there is the need
to open in a second terminal, doing it your way. IOW it's not possible
to run sudo xfce4-terminal, when the box is unchecked, you need to check
the box and then you get two open terminal windows.

So the misunderstanding isn't about the meaning of the words "checked"
and "unchecked", but the way we set up or sudo commands.

We should assume that sudo usually has got a timeout and will ask for a
password after a while. Less people set up sudo not to ask for a
password.