Have had that happen on deer on more than one occasion. I suspect that either it is not bleeding enough internally to fill the chest cavity up to the bullet holes or shredded lung (etc) tissue plugs up the exit hole and prevents bleeding.
Good example of that was this eland. Perfect heart/lung shot, complete passthrough w/300 grain Swift A Frame bullet. As would be expected, animal did not flinch (2000# critter), but he ran 50-60 yards back into the brush. There was a good blood trail for 20 yards or so from both sides, then tapered off. A mesquite tree a bit farther along looked like it had been generously "toilet papered" w/red paper up to 6' or so above the ground and the animal made it another 10-15 yards before collapsing.
The bullet had taken the entire top off his heart (size of a football) and the aorta with it before exiting. Figured the internal bleeding carried tissue into the bullet wounds, sealing them off and he stopped by the mesquite tree coughing up more tissue before collapsing.
Red spot on shoulder is exit wound and the dark spot about 6" above and slightly left is where my second bullet lodged. I made a hasty poor shot as he ran into the brush which clipped last rib and traveled just over 30", lodging just behind the shoulder.
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Those A Frames are tough bullets:
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