ובשר בשדה טריפה לא תאכלו

How is it possible to have half an animal kosher
and the other half is Treifah ?

The Pischei Teshuva (Y.D. 110 sk4) brings
a story that actually  happened.
A  butcher Schechted 7 cows. All seemed to
be kosher. He sent 2 ½ cows to the shop
(Yatkeh) and the rest he kept at home. After
the 2 ½  cows were sent away (Porush) he
discovered one stomach(unknown from which cow)
was pierced (Treifah)
There are two important rules in רוב .
כל קבוע כמחצה על מחצה
At the place where Safek originated  we don’t follow majority.
כל דפרוש מרובא פרוש
If the object left original place, we do follow majority.
The two whole cows at the Yatkeh, (Porush) we follow majority
(6 out 7 are kosher) and are kosher
The four whole cows at home, (Kavua) we don’t follow majority
and are Treifah.
The two Halves, we have a three way Machloke, if both are 
kosher or both are Treifah and the Pri Chadash who holds , 
the half at home (Kavua) is Treifah and 
the half at the Yatkeh (Porush) is kosher.