Edited by lymon at 2016-2-29 16:09
You can't, This is the point of OpenELEC . it is an embedded operating system built around Kodi..also to prevent people from messing around with the main filesystem and break things and then start complaining it doesn't work (anymore)
It is designed to be as lightweight as possible in terms of size and complexity.
You can put/load necessary files in /storage (and /storage/.config) , which is writable and can be used to load/start modules or additional software packages.
Modification of root password (and adding/changing other things to the readonly filesystem) can only be done by compiling Openelec yourself or by using this method:
http://wiki.openelec.tv/index.php/Mksquashfs_Add-on_how-to