Arachin, Chapter 1, Mishnah 3. The chapter's opening two mishnayot sorted out three distinct questions: which people are able to pronounce an erech vow, which people another person may pledge the erech of, and which people another person may pledge the damim of, damim being a person's actual value, the price he would bring if he were put up for sale. Every category listed there works for damim, and the reason is straightforward: each of those people carries a genuine price in the marketplace. Our mishnah crosses over to the other column and introduces individuals who have no place in such a pledge at all.
Two people with no market price
"Hagoseis vehayotzei lehareg": the goseis is a person in the final stage of life, the one whose breathing you can hear coming to its end. The yotzei lehareg is a person whom Beit Din has sentenced to death and who is being led out to his execution. Once that verdict has been handed down there is no reversing it, no pardon and no way back.
Concerning such a person the mishnah teaches "lo nidar": no pledge of his damim is possible. Bring him out to the market and not a single buyer steps forward. His life has effectively ended, and a slave whose life has ended is of no use to any purchaser. With no price hanging on him, the vow has no figure to fasten onto.
"Velo ne'erach": an erech pledge concerning him is equally impossible. The Torah presents an erech assessment as a procedure in which the one whose erech was vowed stands in front of the kohen and is evaluated. Someone in his last moments is incapable of standing; his suffering and distress are too great for him to present himself that way. Since he cannot be put through the kohen's assessment, no erech vow attaches to him.
Rabbi Chanina ben Akavya: a sum the Torah already fixed
Rabbi Chanina ben Akavya's ruling: "ne'erach mipnei shedamav ketzuvin." He accepts the opening clause but disputes the closing one. To his mind a condemned man being led out to die can indeed have his erech pledged, since the Torah itself already established the figure. The erech amounts are fixed brackets, and nothing about the particular individual shifts them: not his health, not his personal situation, not the amount of life remaining to him. He belongs to his bracket, and a vow of his erech is binding.
Then comes "Aval eino nidar," a pledge of his actual worth is impossible, "mipnei she'ein damav ketzuvin," because there the Torah sets no number. That amount depends purely on a buyer's offer, and no one would hand over money to acquire a man on his way to be executed. His market value is zero. On this view the erech pledge succeeds precisely because it was never tied to a buyer's estimate at all; it rests on the table of amounts the Torah spells out for us.
Rabbi Yose: what such a person can still do
Until this point the argument, between Rabbi Chanina ben Akavya and the first Tanna, was about whether a dying man or a condemned man can serve as the object of these vows. Rabbi Yose turns the question around: is such a person still able to make vows of his own?
His words are "noder uma'arich umakdish." Rabbi Yose holds that all three remain open to him. He can vow another person's damim, he can vow another person's erech, and he can consecrate his own property to the Beit Hamikdash, with death only moments away. Such commitments bind him the moment they leave his lips, and while breath remains he retains the capacity to obligate himself. He is accordingly required to pay the market price of the person he vowed, or that person's erech amount, or whatever he consecrated to the Beit Hamikdash.
"Ve'im hizik, chayav betashlumin." And if he caused damage to another person's property, he bears liability for it, and the payment is collected from his estate.
On this final clause the Tanna Kamma parts ways with Rabbi Yose. In his opinion damages are not collected from a person's estate once he has died. While he is alive the money can be claimed from him, but at the moment of death his property passes on to his yorshin, his heirs, and the claim does not follow it there.