Bullet Fragmentation and Expansion
Fragmentation in modern lead rifle bullets is a result of their design, the intent being that the front portion of the bullet expands to almost twice its original diameter. However, one consequence of this expansion is that particles of lead - a soft metal - erode from the bullet's tip as it strikes and travels through its target. This is a concern for humans and animals eating any portion of an animal shot with lead because these fragments are often too small to notice during butchering and comsumption.
The mule deer in the below x-ray was struck by a lead bullet in its spine, at which point it completely disintegrated into hundreds of fragments (black specks seen throughout the image).
Rapid, controlled expansion of a rifle bullet is necessary so that its kinetic energy is transferred into the tissues of its target. Because lead-free bullets do not fragment like lead-core bullets, they retain a greater mass, which enables the bullet to transfer more energy to its target: in other words, the bullets hit harder through more of the animal. Additionally, lead-free bullets often pass through an animal increasing the intensity of the blood trail thus increasing the odds of a successful recovery.