To put it simply, once your punishment is up, you enter what's known as a reform period where you are unable to earn loot. How long this reform period lasts is dependent on your behavior. Once you start showing consistent improved behavior, then you should be able to earn loot again. Also, how long you have to showed improved behavior is dependent on how harsh your punishment was. For a chat restriction, it tends to be somewhat short. If you want more information, you can read this guide.
https://support.riotgames.com/hc/en-us/articles/209939463-Hextech-Crafting-Restrictions
I know this is pretty vague, but unfortunately this is really the only information that has been made public. I have seen it be reported that it takes somewhere around 35 and 70 games for this reform period to end for 10 and 25 game chat restrictions, respectively. However, this is simply an observation, not an absolute truth.
Hope this helps.