Code Igniter, as other frameworks and libraries, should not be change manually, because you lost the posibility of doing updates to your system (If you update your system, public $final_output; will change to private $final_output; and you need to do the change again).
In this situation is only one change needed, but think that you change several more lines, will you remember all the changes to do it again?
My recomendation, open a issue in Code Igniter bug tracker https://github.com/EllisLab/CodeIgniter/issues comment your situation and ask for help. If despite all, you need to do the change, write a patch file containing the change and put it in the same folder of the original file with a descriptive name. In this manner you can apply the patch every time you update your system.