I've seen it, done it myself, directed it to be done by my DMs. Not often, but it happens. True story from my store from a dive years ago that I posted in the Power Scuba thread:
We're diving Farnsworth Banks at Catalina (deep reef for the uninitiated - top is 60 feet and steeply slopes down). I'm the in-charge deck DM. I have a DM on the bow suited up to jump if necessary and another DM about to get in the water to do the dive with one other person. Diver jumps in the water and his AIR2 immediately begins free-flowing. I'm yelling down to him but he either ignores me or can't hear me as he kicks to the bow (maybe 40 feet). I yell up to the bow DM to shout down to him. (Diver is either diving by himself or catching up with his buddy. Can't recall which.) Diver still doesn't respond and dives down the anchor line before bow DM (wetsuit only - no tank or weights) can jump. I instruct my about-to-dive-DM. "Go down and find the guy with the bright green fins and check his air. Bring him up if necessary." My DM jumps in and heads down the line and catches up with the diver in question at 100 feet as he's heading deeper. (Also recall, at Farnsworth, we'd try to set a depth limit of 100'.) DM grabs his fin and gets his attention, motions to check air pressure. Diver doesn't look at gauge and signals "OK". DM shakes head and motions again and this time diver checks. He's got a little less than 300psi (this is less than 3 minutes into his dive.) DM grabs hold of diver's BC and signals "You and I are going up". Diver nods and they ascend. At about 80 feet, diver sucks his tank dry and DM hands him DM octo. They continue up. DM tries to slow them down to do a safety stop but diver is a bit anxious and keeps kicking so they miss the safety stop and pop up (both OK) just off the bow of the boat. My DM escorts diver to the swimstep of the boat. After a short calming-down period, we review the dive with the diver, suggest he sit the next one out (and perhaps the rest of the day), and tell him that if he wants to do dive #3 or #4, he'll go with one of us.
There is absolutely NO doubt in my mind that if we didn't have the mindset about safety that we do, and didn't have the policies and procedures in place that we do, that that diver would have likely died on that dive and we prevented that.
So that's why we chase. We think we can prevent an accident or save them. The trick is making sure you don't cross that point-of-no-return where you become the second victim. No an easy decision to make.
- Ken