Resolving hostage situations

If a thug is holding a person hostage and using her as a human shield, is there any way to resolve the situation without killing anyone?

I tried to aim for the arm or leg, but the shooter always ended up dead or killing the hostage. Is it possible to catch him alive somehow?

Nope, by the time it's come to a hostage situation, the bad guy has to die. If you wound him, he'll stagger and then kill the hostage if you don't finish him off.

Sometimes you can tackle the bad guy (or fire a warning shot) before he gets to the hostage standoff stage, but there's no benefit to doing so. You'll just see a slightly different cinematic for the resolution (wherein he gets loaded in a paddy wagon instead of a hearse)