What are the reprocutions if any if a civil servant engages in illegal demonstartions

according to US law/the constitution how can a government agency deal with a civil servant who participates in an illegal demonstration or riot. I am under the impression that in order to have a lawful demonstration or protest consent must be taken from the proper authority. Also what is the case if said demonstrations and/or riots involve destruction of private and/or public property and/or endanger the public. If you could also add where you got the laws or regulation that support what is said above I will be forever grateful

He can be fired...and that often happens.

What is the actual issue you are concerned about, or is the more of an academic issue?

this is an academic study... I'm not an American and I'm trying to support my study with what the situation is in the USA... if anybody could help direct me to which articles in the law/constitution would support this situation in terms of what can the government agency do with the delinquent employee I'll be forever grateful