Although the Bible does not mention such a cord, it does say that he should wear bells “and not die” (Exodus 28:33-35) This has been interpreted as meaning that someone must listen outside the Holy of Holies for the bells. As long as the priests outside could hear them tinkling, they would know the High Priest was still alive. But what if the sound were to cease? Would that mean he was dead? If so, how would they get the body out, since no one else is allowed to enter? The Bible is not explicit about this eventuality, but the practical solution supposedly contrived by the ancients was to tie a cord around the priest’s ankle just in case. If the sound should cease, those outside could tug on the rope to verify that he was still conscious, and, if necessary, pull him out quickly without defiling the most holy place. Such a tradition is noted in Zondervan’s NIV Study Bible, 1985 as a note to Exodus 28:35, but I have found no reference to it any of the other printed resources at my disposal, including the Encyclopedia Judaica, Josephus, Edersheim and the Talmud. It is mentioned on a huge number of websites (both Jewish and Christian), but none of the several I checked contained any reference for what is usually just presented as fact.
Joseph Good of Hatikvah Ministries, among others points out that the bells were attached to the robe of blue cloth (Exodus 39:22-24), worn under the ephod, whereas the priest wore only the linen tunic, sash, turban and undergarments to enter the Holy of Holies (Lev. 16:2-4), so he would not have been wearing the bells. (They were worn in the Holy Place, but not the most Holy Place).