As stated above -- halachic death would be when there's irreversible heart cessation.
However, your intuition is somewhat correct. See this related question. Once the patient's heart is removed, there is no longer a chezkas chai -- presumption of living -- and thus the odds of success have to exceed fifty percent to allow heart transplants. (Rabbi Unterman ...
Bereishis Rabba 14:11
רַבִּי לֵוִי בְּשֵׁם רַבִּי חֲנִינָא אָמַר, עַל כָּל נְשִׁימָה
וּנְשִׁימָה שֶׁאָדָם נוֹשֵׁם צָרִיךְ לְקַלֵּס לַבּוֹרֵא, מַה טַּעַם
(תהלים קנ, ו): כֹּל הַנְּשָׁמָה תְּהַלֵּל יָהּ, כָּל הַנְּשִׁימָה
Breathing is required so that we have a constant reminder to thank Hashem for our lives. (I once heard that is the reason a ...