This isn't correct. A co-leader can't demote or kick a co-leader.
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If a leader quits (leaves clan) without promoting anyone to leader, then the next rank with the highest trophies is automatically promoted to leader. If the leader just goes MIA (inactive), then your best bet is to start a new clan. In that scenario, you probably wouldn't want to promote more elders to co-leader because you'd just have a bunch on people running the clan with limited authority (i.e. can't demote or kick co-leaders).