In the context of this phrase it means: to put an end (exterminate) to a way of living that they've been trying to build. That is, instead of doing it properly, they ruined it.

Suggestions:
وينتهي بهم الأمر إلى وأد الحياة التي يعملون لإحيائها
- they end up extinguishing the very way of living which they have been trying to build.
- they end up ruining the very lifestyle which they were seeking to create in the first place.


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Note added at 1 day 13 hrs (2017-11-16 09:09:02 GMT)
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I just found the article on the web. It talks about 'the system of living' and its aspects, by which humans need to abide. In this case it means:

They end up degenerating the very living system which they were seeking to construct.
They end up devolving the very living system which they have been trying to develop.

Note that this aspect is on the ethical factor, hence the use of degenerate/devolve.