While the status of foreigners is regulated by the Armenian Law on Foreigners, immigration-related offenses and penalties are generally contained in the Code of Administrative Offenses. Namely, article 201 of the Code provides penalties for visa overstay and other illegal stay of foreigners in Armenia. You can find more information on visa overstay, including applicable penalties, here: https://armenian-lawyer.com/visa_requirements/.
Article 201 also provides penalties for those individuals or legal entities who invited a foreigner to Armenia and failed to honor their commitment to cover the living, medical, travel and other expenses of the foreigner in question. This penalty of 50,000 to 100,000 AMD (approximately, US$ 105 to 209) is applicable only if the person who issued the invitation letter explicitly took a commitment to cover the expenses.
The same article provides penalties for Armenian employers who use foreign employees without valid work permits or residence permits. Because the Armenian government has not yet (as of 2018) implemented the system of work permits, in practice Armenian employers must ensure that a foreign employee reports to work only after a residence permit is issued. Failure to do so may result in a fine for the responsible executive officer of AMD 100,000 to 150,000 (approximately, US$ 209 to 312).
The Code also requires foreigners who hold a residence permit to register their address with the local police office within 15 days. If the foreigner changes his place of residence he has to report it to the local police office within 7 days. Failure to register the address may result in a fine of AMD 3,000 (approximately, US$ 6).