The claims queue
A campaign sends. The customer writes back. That reply sits in the claims queue with the message that went out, in the same thread, until someone on the workspace takes it.
Taking a thread is how a person owns the conversation. From a selection you can also hand threads to someone else. On a phone, the queue opens as cards. A filter keeps only the threads that include a call.
Opt-outs stay on the account. A STOP is not a thread to work. It is a person who has left the list.
On a workspace with more than one person, the queue is how the replies get an owner instead of sitting in a shared pile with no name on them. Add people from the account page before the replies start, if more than one person will answer.
A personal campaign is the exception: those replies come back assigned to the person who sent the campaign, rather than waiting for someone to take them.