We present a theory of non-steady state free radical polymerization kinetics at high conversions where entanglements are present. Our immediate aim is to explain apparently infinite experimental living chain lifetimes at conversions that are high, but very far from the onset of glassy behavior. In these "posteffect" studies, the time dependence of the total number of living chains is measured, after the steady state is interrupted by switching off primary radical production at t = 0. We find that infinite lifetimes are inevitable in posteffect when entanglements are present. Our starting point is a previous theoretical study of steady state entangled polymerizations according to which the principle termination mechanism for the majority long entangled chains is provided by the small population of short mobile unentangled chains. In posteffect, we find that the entire short living chain population disappears after a time scale tau(short) approximate to z/v(p), where z is the conversion-dependent threshold for entanglement-dominated reaction kinetics and v(p) is the rate at which monomers add to a living chain. For t < tau(short) the situation is essentially unchanged from steady state and the terminated fraction R-t grows linearly in time t. But by tau(short) all short chains have either grown to become long or have terminated through interpolymeric radical-radical reactions. Consequently, the net termination rate is drastically suppressed for t > tau(short), decaying as 1/t(1/2). Correspondingly, R(t) increases as t(1/2). At the longest times, t > tau(rad), where tau(rad) is the mean steady state living chain lifetime, termination saturates : in the presence of entanglements, the living population is infinitely long-lived and the final terminated fraction is of order (z/(N) over bar)(1/2) much greater than 1, where (N) over bar is the steady state living chain length. Our intermediate time prediction, R(t) similar to t(1/2), is consistent with experiment.