General case of survivors fallacy:
Looking only at/for things that didn't fail skews your perception. This may lead you into an untested and thus failure intolerant behaviour.
The usual example is observing planes returning from air combat:
"Do you need to increase armor in places where the returning planes were hit?" Supposedly it's where planes are likely to be hit.
However the answer is counter-intuitively "No, because that's where planes are likely to be hit and survive." So hits there are survivable anyway.
You achieve real results, when you increase armor in places the "survivors" have not been hit, because that's where the "non-survivors" were hit.
For your case (singular):
Under the precondition of moving a single person into an area with incidents leading to deaths.
Do I need to move into a sub-area that has not been hit by an incident?
No, for those sub-areas you simply have no conclusive data.
Instead you need to move into a sub-area where incidents do happen but don't lead to deaths. The goal is not to have no incident but to survive it, in case it happens, right?
If you don't want the incident to happen, you shouldn't move into the larger area in the first place!
For your case (plural):
If you want to move a statistically relevant number of people into the area where incidents are survivable, you need to first check, if the reason incidents are survivable is low population density in said area.
If incidents are survivable in low density population areas, moving people in wouldn't make the people safe but the area unsafe.
Another view on things:
If there are 1000 people in the larger area, of which 20 died in the last incident, then there are still 980 survivors left to tell the tale. Is it safe, because more people survived than died?
Surely most of the 980 people weren't even close to the 20 that died, when it happened. Does it become any safer, if you just ask those?
Can you ask the 20 dead people, if they'd still consider it safe?
Bottom line is, you'll feel safe as long as you ask survivors, who didn't witness the incident. Since you can only ask survivors, it's probable they didn't witness the incident.
Hence, Survivors fallacy.
Others have mentioned other fallacies. I don't want to repeat them in detail. However I do see that they apply as well. So here's a compilation and the aspects why they apply and why they are different:
- Survivors fallacy: Concentrating on favourable results only.
- Texas Sharpshooter fallacy: Choosing a sub-sample in hindsight.
- Hot hand fallacy: Interpreting random variation of results as indication of probability distribution, especially when looking at most recent history.
- Small numbers law: Relying on insufficient data.
- Base rate fallacy: Underestimating the importance of general information in favour of more specific information.
There's another well-known fallacy that I originally mistook for "Hot hand". Now that I think about it, it actually doesn't apply:
- Gambler's fallacy: Misunderstanding the law of large numbers to mean that independent events would even out in the long run.
It's kind of inverted Hot hand fallacy:
Falling for "Hot hand" you'd bet on what happened most often in recent history, because it seems more likely.
Falling for "Gambler" you'd bet against what happened most often, because the opposite seems in need to even out in the long run.