Linux runlevels and chkconfig

Question

I know this an old question but I am having a tough time in understanding the linux runlevels w.r.t gracefully stopping and starting a service. For suppose consider myscript service is configured to auto-start after a system shutdown/reboot. Below is the output of chkconfig command (RHEL 6.5x):

[testfolk@jomohost ~]$  sudo chkconfig --list|grep myscript
myscript             0:off   1:off   2:on    3:on    4:off    5:on    6:off

I understand that myscript service auto-starts on system startup. But what takes care of it's gracefull stop/shutdown task. What if myscript is a delicate service and need to be stopped at any cost before any reboot/shutdown or the application gets corrupted. Is taken care of by default ?

Can I configure it something like below to do a graceful auto stop:

[testfolk@jomohost ~]$  sudo chkconfig --list|grep myscript
myscript             0:on   1:off   2:on    3:on    4:off    5:on    6:on

My assumption of above configuration is the myscript service gets auto stopped on invoking init 6 or init 0. Is this a valid config, I can be completely wrong, please advise. I searched as many articles as possible but all of them were talking about auto-start of a service after a reboot or shutdown but not auto-stop. I am not sure if I am understanding this whole thing correctly, pls help if you have any info!

Thanks in advance for your time!