My Twin Lyrics

Lyric discussion by AlfB 

Cover art for My Twin lyrics by Katatonia

I think the earlier messages are reading too much into it, this sounds like someone who's suffering the agony of relationship breakup - probably in a protracted way:

"are you strong when you're with him"

...as though they've had a "we need to talk" discussion and she's confessed she's fallen for someone else, that their own relationship doesn't fulfill her anymore.

"the neck, and then the chain the head is hung in shame"

I think this is much more straightforward than suggested too. If you're feeling guilty you avoid eye contact. She's come to break up with him, and she can't bring herself to look at his face, her gaze is lowered, and draws down as the news settles in - so first her stare is directed at his neck, then falls to the 'chain' hanging below his neck.