if i login in ubuntu core system by root, then start a application in deamon. then exit the login. the shell show “exit , there are stopped jobs”, 
if i run exit again to general user login, the ubuntu core reboot automatic. show below log
how did you do that ? the root account password is locked and /etc/passwd and /etc/shadow are on a readonly image that you can not modify … did you sudo -s or sudo -i to become root ?
again, you need to describe in more detail what you did there. on ubuntu core daemons typically only come from snap packages (and start automatically or by using the snap start/stop commands)
i use sudo snap run --shell “snap apps name” to login root.
$ sudo snap run --shell test.init
root@localhost:/var/lib/snapd/void#
root@localhost:/var/lib/snapd/void#
root@localhost:/var/lib/snapd/void#
root@localhost:/var/lib/snapd/void#
root@localhost:/var/lib/snapd/void#
ok, so you were just entering an application sandbox and did not actually become root (well, technically you are root, but since you are inside that app sandbox you are only root for this application)
now … do you see the informational message about stopped jobs every time you leave that sandbox ? i.e. is it reproducable ?
my assumption would be that your system got a core or kernel update which will trigger a reboot by design, but since you were in the sandbox you did not get the notification message that gets sent to all terminals, so your application jobs (inside the sandbox) were stopped by the reboot process and the sandbox shell tells you about it when you exit.