A critical non-Hermitian skin effect (CNHSE) was recently discovered in which the eigenenergy spectrum of a coupled system comprising two 1D non-Hermitian (NH) chains exhibits an abrupt change when the length of the system increases beyond a critical length. Here, we overturn the conventional wisdom that multiple chains are required for the CNHSE by showing that a similar abrupt transition in the eigenenergy spectrum occurs with increasing length in a single finite 1D chain when the two ends of the chain are connected by a weak terminal coupling to form a closed loop. We illustrate this phenomenon using the classic Hatano-Nelson and Su-Schrieffer-Heeger NH systems, and show that it can co-exist with the conventional CNHSE in coupled NH loops.