Who can create a chat depends on your group settings (see Admin->Settings->Features->Chats).

Any group subscriber can "join" an ongoing chat in that group. A "private" chat, with only a subset of the group, is not an available feature.

Chats can later be closed or deleted. Closed chats remain visible but you can't add to them.

Closed chats can be reopened, if desired. Once deleted, they are gone.

See also https://groups.io/g/GroupManagersForum/topic/23482824#10264