(A/N: I made this K+ mainly because I had no idea whatsoever how to rate it . . . better safe then sorry. FYI, this is in a universe where The Doctor didn't regenerate at TEoT, so it's still Ten, though I'm not giving an explanation for that . . . Feedback is always appreciated!)
The Doctor waited. At first, he kept going like normal, like he always had. Then, in a traumatic incident involving a kettle, a Dalek, and a pear, his regeneration cycle was damaged. No more could he come back from death. He started being careful, stopped travelling, he even let go the habit of taking up companions. The Doctor moved the TARDIS to London, where he knew that he would be easily found. There The Doctor sat, doing nothing but waiting. Waiting for him to return, waiting for The Master.
The Doctor never gave up hope, not like he had in the past. He had learned that The Master never really left. Not for good. He always came back, one way or another, no matter what happened. At least, that's what the Doctor told himself. It was enough to keep him waiting, that sliver of hope, that he would return, because The Master would return, The Doctor knew that for a fact. Didn't he?
Despite his efforts, his health wore thin. There was only so much waiting The Doctor could do. He was old and decrepit, an unmoving husk of a time-lord sitting by the TARDIS console, which was also damaged and slowly dying. The Doctor had to face it, his time was nearly up. When The Master finally did come back, he wouldn't be there to greet him. Still, in his final hours of life, he waited, and wished with all his hearts that he could see The Master just once more.