When one actor left the show, a new one could replace him through this biological process that only seems to work with Time Lords. It is like a cat who is said to have 9 lives; in the Who universe, a Time Lord has 12 re-generations, or 13 lives in total. In reboot Season 8, Capaldi becomes the 13th and final Doctor according to the show's own canon.
Now, I take the position that the producers should embrace the challenge of having the "last" Doctor because it would be a trans formative narrative for a complex character that is still shrouded in much mystery. But the BBC still calls the new Doctor only the 12th. And the producers seem to agree.
But with such intense fandom, and the regeneration process one of the few ironclad rules of the show, this is a potential Jump the Sharknado moment. Some believe that the producers will just concoct another cycle of regenerations (like some believe may have occurred during Matt Smith's final episode in Season 7). But that does not show respect for the original material, and the legacy of the prior creators who kept the series alive, fresh and interesting.
It is a very simple proposition when the current Doctor leaves the show. He dies. But what panic would occur in London if there was no new Doctor? Probably not much, for you see it would be just as compelling for the show to turn its axis point (temporarily) to the biggest mystery of all: who could replace the Doctor? The candidates could be more vast than the standard collection of Who villains. Another Time Lord? Another alien species? The Doctor's "daughter?" Or his last companion? For Doctor 2.0 to exist in the context of the original canon, he or she would have to be an extraordinary being (alien) compatible with Gallifreyan biology and who would inherit the one item that would bind the new series with the old: the Doctor's pocket watch. The watch contains all the memories and information of the past time lords. It can imprint them on Doctor 2.0. Problem solved from a writing continuity standpoint.
But I find this solution highly improbable. It is too detailed; too "insider" for a network executive to grasp the nuisances. The production company has the brand of the Doctor and does not want to dilute it with a successor, even if he or she is a worthy one.
It is theme for successful shows, including sci-fi epics, that if set canon is violated, the trust with their audience is breached because successful sci-fi shows rely heavily on their own mythology to support the fantasy. Doctor Who is fast approaching such a breach. How the show runners will cope with this event is still unknown.
