Midrash su Levitico 11:39

1) (Vayikra 11:39) ("And if there die of the beast which it is yours to eat, he who touches its carcass shall be tamei until the evening.") "And if there die of the beast": "die," literally, (and not ever min hechai). "of the beast": There is that of the beast which confers tumah, and there is that of the beast which does not confer tumah — to exclude a treifah (an organically defective animal) which was slaughtered, (the shechitah "cleansing" it). But does this not follow (even without a verse)? viz.: If we find with an unclean beast that it is not the designation ("tamei") that forbids it to be eaten which brings it to a state of tumah, but its death — treifah, too; it is not the designation ("treifah") that forbids it to be eaten which brings it to a state of tumah, but its death, (but if there was shechitah before death, it remains clean of tumah). Or go in this direction: An unclean beast was forbidden (for eating) before its death, and a treifah is forbidden before its death. Just as an unclean beast is not cleansed (from carcass tumah) by shechitah, so, a treifah is not cleansed by shechitah. It must, therefore, be written "of the beast." There is that of the beast which confers tumah, and there is that of the beast which does not confer tumah — to exclude a treifah (that was slaughtered) by shechitah.

2) Of what is this (Vayikra 11:24) speaking? If (of beasts) in their death (i.e., neveilah), this has already been stated (viz. Vayikra 11:39). If of flesh torn from a dead animal, this has already been stated below (see Chapter 6:6). What, then, must it be speaking of? Ever min hechai.

2) A different argument: An unclean animal may not be eaten, and a treifah may not be eaten. Just as shechitah does not cleanse an unclean animal (from carcass tumah), so, shechitah should not cleanse a treifah (from carcass tumah).