Players will often find Common Enemies in the open world while exploring, or in Domains and Spiral Abyss. These enemies may occasionally drop Common Ascension Materials. They always drop a varied amount of Mora upon killing them, although usually in small amounts and provide very little Character EXP.
There is a hypothesis that each group of Common Enemies that you can encounter in the open world will respawn exactly 12 hours after the time of discovery. For example, if you found a group of Hilichurls and then 11 hours 50 minutes later decided to kill them and come back to the same spot after additional 10 minutes, the group will respawn. Since this is a hypothesis, it's still not proven but it's very likely to be true based on current data.
There is also a hypothesis regarding daily kill limit yielding drops of 2000 Common Enemies. It is still unconfirmed, but multiple video proofs show that this might turn out to be true.