How to deal with management explicitly asking you to implement a poor solution

I was asked to implement a administrative feature which potentially could have catastrophic consequences and get people fired.

I have suggested a well thought through solution, eliminating accidents and which was backed by all members of the team, only to be thanked for all the effort, and was told after the meeting to continue with the poor, corner cutting solution which I know, that will come back one day and bite the team in the back side.

How to deal with situations like these? It does not sit well with me to put my name under this solution, but I'm asked to do it anyways.