In other words, hubby probably got three good body shots into the bear with a .300 Win Mag (rifle) and that *still* didn't kill the bear. The bear left instead of dying.
At close range, the .300 WinMag bullets probably punched right through the body without expanding, leaving very small wound channels, unless they hit bone.
For something like a bear, you want a big, heavy, hard bullet, one that doesn't expand much in order to get penetration, but has a large surface area to open a large wound channel. 300gr and larger bullets are a good starting point. A good combination would be a heavy .444 marlin or a modern heavy 45-70 in a lightweight, handy carbine. These are both less powerful than the .300 WinMag on paper, but better suited for bear at close range, due to their balistic performance.
Mark