A בריה — a whole creature/unit (an ant, an impure bird, the גיד הנשה, a limb of a living animal, an egg containing a chick) is never nullified, even in a thousand (אפילו באלף); the three conditions of a בריה (having had life, being forbidden from its formation, being whole), the גיד which does not forbid by taste but whose fat does, and worms (תולעים) found in vegetables (Shulchan Aruch, Yoreh De'ah 100 — 4 se'ifim)
בְּרִיָּה — דְּהַיְינוּ כְּגוֹן נְמָלָה אוֹ עוֹף טָמֵא וְגִיד הַנָּשֶׁה וְאֵבֶר מִן הַחַי וּבֵיצָה שֶׁיֵּשׁ בָּהּ אֶפְרוֹחַ וְכַיּוֹצֵא בָּהֶם — אֲפִלּוּ בְּאֶלֶף לֹא בְּטֵלָה. וְאֵין לוֹ דִּין בְּרִיָּה אֶלָּא אִם כֵּן הוּא דָּבָר שֶׁהָיָה בּוֹ חִיּוּת, וְשֶׁאָסוּר מִתְּחִלַּת בְּרִיָּתוֹ, וְשֶׁהוּא שָׁלֵם.
A בריה — for example an ant, an impure bird, the גיד הנשה, a limb of a living animal, an egg containing a chick and the like — is not nullified even in a thousand. And it has the status of a beriah only if it is a thing that had life, that is forbidden from the start of its formation, and that is whole.
Shulchan Aruch, Yoreh De'ah 100:1LEVEL 01
Hebrew text of the 4 se'ifim with a fluent English translation. The בריה that is never nullified, its three conditions (חיות, אסור מתחילת ברייתו, שלם), the גיד הנשה and its fat, the בריה lost in the liquid and worms in vegetables explained with practical cases.
📖 StudyLEVEL 02
In-depth pilpul: the sugya of Chullin, the חשיבות of the בריה as דרבנן (Taz sk1) and the nafka mina for a doubt, the analysis of the three conditions, the גיד הנשה as a בריה with no taste but with forbidding fat (Shach sk1), the בריה that melted (נמוח) and the חזקה of ג׳ תולעים, חקירות and נפקא מינות.
📖 StudyLEVEL 03
Comparative tables (the three conditions, recognized / not recognized, גיד with or without 60 against its fat), golden rules, classic pitfalls (ספק בריה, נמוח, ג׳ פעמים, בריה רסוקה → siman ק״א) and memorization of the 4 se'ifim.
📖 StudyLEVEL 04
The practical halacha according to the Shach, Taz, Pri Megadim and Pitchei Teshuva, then the Sephardic poskim (Yabia Omer, Yalkut Yosef, Or LeTzion) and Ashkenazi poskim. Note: the Shulchan Aruch HaRav does not deal with this siman — this is a level of psak, not "Daat HaRav".
📖 StudyAccording to the Shulchan Aruch (YD 100:1), a בריה — a whole creature or unit, for example an ant (נמלה), an impure bird (עוף טמא), the גיד הנשה, a limb of a living animal (אבר מן החי), or an egg containing a chick — is not nullified even in a thousand (אפילו באלף לא בטלה), because of its importance (חשיבות). According to the Taz (sk1), this 'is never nullified' is דרבנן (Rabbinic): מן התורה a בריה is nullified like any prohibition. Nafka mina: in a case of doubt (is it really a בריה?), we have a ספק דרבנן and we are lenient (it is nullified). For practical halacha, consult your Rav.
The Shulchan Aruch (YD 100:1) lays down three conditions. (1) חיות — the thing must have had life, which excludes a grain (חטה) of a prohibited substance, which never had life. (2) אסור מתחילת ברייתו — it must be forbidden from the start of its formation, which excludes a kosher bird that became נבילה and the שור הנסקל, which were not forbidden from their formation. (3) שלם — it must be whole, such that if it is divided its name no longer applies to it (שאם יחלק אין שמו עליו), which excludes חֵלֶב (forbidden fat); and it must actually be whole. For practical halacha, consult your Rav.
No. The גיד הנשה is indeed a בריה (it had life — Shach sk1), so it is not nullified as a בריה. But the sinew itself has no taste (אין בגידים בנותן טעם): it therefore does not forbid the mixture by its taste. However, its fat (שמנו) does forbid, and one needs 60 against it to permit the liquid (YD 100:2). A thigh (ירך) cooked with its גיד: if one recognizes it, one discards it and the rest is permitted if there is 60 against its fat; if one does not recognize it, the pieces are forbidden but the liquid is permitted if there is 60 against the fat. For practical halacha, consult your Rav.