Apart from the fact that this is logical fallacy, all your examples are not civilisation ending scenarios.

If we both are on a cliff face and you fell off, and now you are dangling connected by rope to only me. Standard movie trope.

Now because of your weight my only options are to cut the rope - you die, or wait and we both die. This is more accurate example we are talking about here, not killing poor people because 'crime'.

Also I would like to point out that poor people are not root cause of crime. So you are not tackling actual problem, only applying band-aid solutions. But that's a tangential topic.