A search has been conducted for optically obscured asymptotic giant branch (AGB) stars in the LMC. The results obtained are noted to rule out the presence of sufficient high-luminosity 'cocoon' stars to explain the observed deficit of several hundred luminous AGB stars between the predictions of standard AGB evolution models and the observed luminosity function. Bolometric magnitudes as low as -5 are inferred for these sources; it is suggested that this phase can be triggered at low luminosities, truncating AGB evolution and leading to the observed scarcity of AGBs with M(bol) greater than -6.0 mag.