Background process received SIGHUP from bash when user logged out from X-window

Issue

• Our customer's process which was executed on background sometimes received SIGHUP when the customer logged out from X-window.
• We confirmed the parent process of background process closed by SIGHUP when the background process closed. And, the parent closed by EIO when the background process remained.

• So, we consider that bash does't send SIGHUP to the background process if bash closes by EIO before receiving SIGHUP. Is this thought correct?

• Detail Steps:
  1 log in X-window as not root user
  2 execute gnome terminal
  3 change root user by executing su -

    $ su -
  

  4 execute bash

    # bash
  

  5 execute some commands on background (ex. sleep 1000 &)

    # sleep 10000&
  

  6 push "x" buttons of gnome terminal
  7 sleep process remains OR sleep process closes

• In case of sleep process remained

        ├─gnome-terminal(5272)─┬─bash(5276)───su(5304)───bash(5308)───bash(5336)───sleep(5352)
        │                      ├─gnome-pty-helpe(5275)
        │                      └─{gnome-terminal}(5277)

- bash(5276) closed by SIGHUP.
- bash(5308) closed by EIO.
- bash(5336) closed by EIO.

• In case of sleep process closed

        ├─gnome-terminal(5140)─┬─bash(5143)───su(5170)───bash(5173)───bash(5201)───sleep(5222)
        │                      ├─gnome-pty-helpe(5142)
        │                      └─{gnome-terminal}(5144)

- bash(5143) closed by SIGHUP.
- bash(5173) closed by EIO.
- bash(5201) closed by SIGHUP.