Before a design goes into production, you would want to do some due diligence to make sure the design is robust. Usually, this involves doing as much analysis as you can, and then testing the hell out of the product to find out its failure modes and to make sure that it will not fail under the operating and storage conditions specified.
If I were an engineer in that situation, I would do the analysis on my own, even if it meant my own time had to go in. This would be as much an issue of self preservation as it is an altruistic gesture for the company. Bottom line is, ... if the product fails with that production level, it can cripple the company, hurt stock owners, and I and my fellow coworkers may lose our jobs. Also, doing the analysis is a good learning experience and I often do such exercises on my own anyway just to learn.
If my own analysis revealed a problem, then I would report the problem. Otherwise, I would not mention my work and just sleep a little easier at night.
But, this analysis is a secondary issue. The main question is whether the product/device has been subjected to real world failure mode testing. Have you beaten the crap out of it to find out what makes it break? If you haven't, then you will find out that answer from field data on the real product, which might end up being very costly.
For reference, any design work I've ever done on Navy contracts has always required a detailed stability and sensitivity analysis. Never have we been allowed to say, "hey the system is not linear", or "it can't be linearized", or "it is inherently unstable and hence a stability analysis can't be done or is not meaningful". There is always something that can be done, and we have to do whatever can be done mathematically, even if it is only approximate. But, after all this due diligence design work, the Navy then goes and beats the crap out of the system. This last "gate" is the critical one because mistakes can be made in an analysis but real data does not lie.