Yet another gross gunshot wound question...!

I know modern firearms can over-penetrate through a person and kill someone behind them, but what about a late-19th century rifle?

I have a scenario where Person A tries to protect Person B with his body while Enemies are shooting down at them from a nearby rooftop (3 story building). A will die. The bullets enter his back and exit his chest, becoming dirty shrapnel (deformed bullet, possible bone fragments - eww) that will injure but not kill B. Is this plausible?