Technically speaking, a commune with no written laws is anarchy. Recent examples of anarchist communes would be Catalonia during the Spanish Civil War, and the Ukrainian Free Territory for a short time after the October Revolution.

There have been plenty of societies that did not write anything down and that would not be considered to have "plunged into anarchy". Any number of these worked because people are cultural beings that regulate one another in subtle and overt ways, none of which require written laws.

Also, "laws" come in many different forms: prescriptive, prohibitionary, guideline/suggestion, etc.