Is this a valid sentence?
Degradation: 1. the condition or process of degrading or being degraded.
As used in this context:
"...doing so would bring shame to the family. For fear of degradation, ..."
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Generally, yes. Your usage is correct.
It sounds a bit awkward though, but that may be due to the limited context. As in these examples from Merriam-Webster online, I would tend to expect a direct connection between the passive degradation of something and the item that is being degraded.
Something along the lines of: "...doing so would bring shame to the family. For fear of degradation of the family's honor..."
But then you run into an awkward phrasing with so many 'of's so close together... where I would also rewrite that to be 'For fear of degrading the family's honor...'