The goal of this proposal is to elucidate the evolutinary status of J-type carbon stars by observing their extended dust shells in the far-infrared. There are non-negligible number of cool carbon stars which show low C12/C13 carbon isotopic ratios in their atmosphere (J-type carbon stars), prototype of which is Y CVn. They show no s-process element enhancements, which suggests that they have not experienced the third dredge-up which is the key process to produce carbon stars on the aymptotic giant branch (AGB). The lack of s-process enhancements tends to be interpreted as the sign of them being not on the AGB. However, we have detected a very extended, detached dust shell around Y CVn at 90 and 160 micron with ISOPHOT in our Guaranteed Time (GT) program, HIZUMIUR_REDSTAR2. Our results indicate that the mass-loss rate decreased by about two orders of magnitude in the last 14,000 years. The rapid, great change of the mass-loss rate resembles to those observed toward carbon stars U Hya and U Ant which are known to be on the AGB. Such similarity suggests that Y CVn is also an AGB star. While the formation process of ordinary cool carbon stars on the AGB is relatively well understood now, the evolutionary status of those J-type cool carbon stars is still remains to be answered. In this proposal we plan to study the dust shell of RY Dra, the second brightest J-type carbon star next to Y CVn, both of which have extremely low C12/C13 isotopic ratios (< 5) in the atmosphere, in order to study its mass-loss history. We will examine if RY Dra also has an extended, detached dust shell similar to the one around Y CVn. The results on the two stars will provide us with important information on the mass-loss history of J-type carbon stars, thus would help to understand their evolutionary status. This proposal is an extension of our GT ISO observing program HIZUMIUR_REDSTAR2, in which we examine the structure of extended dust shells around both oxygen-rich and carbon-rich AGB stars in the far-infrared using ISOPHOT.