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Basically, the Valeyard is possibly some kind of CIA bio-weapon, and instigates a plan to replace the Doctor via psychic bacteria infecting the TARDIS connection to the matrix (which are linked to the Doctor also), or somesuch, allowing the Valeyard to, not only replace himself as the Doctor, but any, and every Time Lord he chooses.

His plan goes ahead, and Six ends up cut off in a part of the matrix as a temporal anomaly, with a countdown to his erasure by the matrix. Shit happens, and Six manages to create a paradox by convincing a younger version of himself to travel to the planet from the Time and the Rani, and get a lethal bout of radiation poisoning (which is conveniently not lethal to humans). This paradox traps (and kills) the Valeyard in part of the matrix, and deletes the older version of Six which caused the paradox. Six kinda gets two final speeches really:

I've lived a good life, by and large.
Oh please, spare me th-!
Why should I? You didn't intend to spare me. You were prepared to sacrifice me, and all of Time Lord civilisation, in the cause of your...monsterous, twisted ego. Frankly, I'll die happy, if the last words you ever hear are mine. Words...in praise of the best of times; Peri, Mel...Evelyn...Flip, Mila, Constance, and all the others!
And yet, you'll leave Mel to die in your TARDIS!?
She won't die! That radiation won't kill her. It's only deadly to Time Lords. The TARDIS will land on Lykursha...Mel...will survive. And the Time Lords will survive - imperfect though they are - at least they won't become insane manifestations of you!
You can't let me die! I'm part of you!
...You're nothing to me!
What about your precious moral scruples!?
...They died with me.


Then, leading into the Time and the Rani, Mel falls unconscious because of the radiation, Six gets irradiated, and his final speech goes:

-What I was going to say, was that I'm afraid it's deadly to Time Lords...oh...oh so that's it. Oh well...*groans in pain*...I've had a good innings...all those lives I've lived...I hope the footprint I leave will be......light...but, apposite.*grunts in pain*...
It's far from being over.
Who said that!? Who is that!? Who's...there? Change...I feel it! Yes. I will regenerate!
Yes. I will regenerate!
Our future...is in safe hands!
...[Lots of whoosing noises]