This is a song about suicide. IMO the other interpretations go for the obvious (except the currently highest rated one, but I still think it's not completely right).
VERSE 1:I tried to face the fight withinBut it's overI'm ready for the riot to begin and surrender
The person this song is about was unable to conquer their inner issues (likely mental illness or addiction) and now time has run out with no hope for a solution, they now have to face the consequences of their failure. They have no resolve to fight against them and give in to negativity and become consumed with hopelessness.
I walked the path, it led me to the end, rememberI'm caught beneath with nothing left to give, forever
They blame themselves for where they have ended up because they were fully aware of the inevitable conclusion of their harmful decisions yet they were too weak to stop themselves from making those decisions (like taking drugs/drinking or letting their life fall apart due to depression or some form of mental anguish). Now they are completely trapped underneath the weight of the world after having buried themselves. The rest of their life they will live with the incredible guilt and feelings of helplessness while also feeling like they have failed the world due to their uselessness ("nothing left to give")
CHORUS:When angels fall with broken wings
This is where I really disagree with the present interpretations. To me, the line actually means "IN A WORLD where angels fall with broken wings," as if to demonstrate the depth of the world's corruption and hopelessness by suggesting that the state of humanity is so dire and so cold that the purest beings in existence are crippled by it and are powerless to save us. The subject of the song sees the world as incredibly hostile and antagonistic because their own issues make them (feel) persecuted by mere existence.
I can't give up, I can't give in
Many apparently think this is about strengthening resolve but I believe it's the exact opposite. It's about being completely and (I keep using this word) hopelessly trapped in a situation with no solution. They can't find a way to go on by themselves but neither can they right whatever wrongs they have done and either way will be forced to see themselves as villainous.
When all is lost and daylight ends
"When I have died and everything is gone," daylight being a metaphor for consciousness
I'll carry you and we will live forever, for ever
This line determines that the subject of the song is in fact speaking to someone. The "you" in this case seems to refer to whomever might be reading their suicide note (since the song seems like that's what it is, diagetically). They're saying in their ideal version of the afterlife they would have the strength to "carry" who they are speaking to instead of being weak and unreliable and that they would be able to be happy together forever, however because it's such a naive and fantastic existence it implies that the singer knows deep down that it could never happen.
VERSE 2:Grey skies will chase the light away, no longerI fought the fight, now only dark remains forever
Basically the same as the first verse. Singer was troubled in life and it ruined their opportunities to be happy and fulfilled (grey skies chasing away the light), however that won't happen anymore (because they're going to die/are dead). They struggled to survive and be productive but it doesn't matter now (because they're going to die/are dead).
Divided I will standAnd I will let this end
They are singled out because of their issues and the darkness that is taking hold of them (or has done so their entire lives and is now running over). They are standing up and building up the courage to do what they should have done a long time ago and kill themselves ("I will LET this end," as if they are allowing it rather than forcing it, implying it is a natural conclusion to their life)
CHORUS AGAIN
BRIDGE VERSE:The sun begins to rise and wash away the sky
The sun comes up and the world is now going on without them, oblivious to their struggles and suicide.
The turning of the tide, don't leave it all behind
They are telling the "you" person from before that they shouldn't be like them, don't make the same mistakes they did. They should stay on Earth and live a normal life and move on without the singer.
And I will never say goodbye
They're saying that even if they couldn't function in life and wish to die, that doesn't mean they're turning their back on anyone or anything. They don't want whomever they are communicating with to feel hurt or lost because they are gone and they don't want to make them feel like it's their fault. They aren't going to say goodbye because they want to slip away from everyone and everything on earth as quietly and insignificantly as possible because deep down they don't want to hurt anyone.
CHORUS AGAIN
Well, that's how I see it. Pretty morbid but it's the interpretation that fits the lyrics the best in my opinion.
