Quick, What does 沉沦的人 mean?
I was embroiled in a rather serious discussion with someone on Skype, and she said something like, "Why not let me to be a 沉沦的人" and I can't find a definition that makes sense on the internet!

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沉沦kinda like your word sink, sinking of life, give something up , depressed in the gloom mood.

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沉沦：to get yourself lost, to indulge in
so, a "沉沦的人" means somebody who gets himself lost and indulges in something, depressing himself.

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The specific meaning depend on the context. 
I guess what he wants to express is " let it go ".