We present evidence that PG 1159 stars could harbor He-rich envelopes substantially thinner than those predicted by current evolutionary models with current estimates of mass loss, which may be attributable to an extensive mass-loss episode during the born-again AGB phase. Specifically, we show that the models with thin He-rich envelopes predict remarkably large magnitudes of the rates of period change of the trapped and untrapped modes observed in the pulsating star PG 1159-035. This is a consequence of the much shorter evolutionary timescale of the models with thin He-rich envelopes during the low-gravity PG 1159 regime. Our findings are particularly interesting in view of the suggestion of an evolutionary link between the helium-deficient PG 1159 star H1504+65 and the recently discovered white dwarfs with almost pure carbon atmospheres.