For your assertion to be true / accurate then a Cllr ceases to be a Cllr on the whim of a committee.
It should be patently obvious that this cannot hold true.
A Cllr, whether elected or co-opted, remains a Cllr until the next election, or they resign, or they fail to attend for 6 months, or they are disqualified by criminal conviction.
That’s all that changes a Cllr to a member of public. Apart from that, a Cllr is a Cllr.