Once you are defeated you don't play any more turns. You get the final turn so you can see your final battle (or whatever happened that eliminated you). But, there is nothing for you to do, and the game will not wait for you any more. Many players set themselves to AI rather than wait to be vanquished, but I guess Gaius Julius Carulus really did stay to defend the city to the death.
It's too bad he wasn't a commander, though

Your troops will rout if you have no commanders in the fort to lead them. Otherwise, they can't rout until something happens to them. On a related note, if you try to break siege and fail, any troops that routed will go into neighboring provinces if possible and die if not possible. They won't go back into the fort, and if you didn't leave someone behind inside the fort, it will be immediately captured.
Troops routing defending a fort is silly, but that's how the game works. It's actually possible for them to rout into neighboring provinces, or at least it was in dom2 - talk about frustrating for the sieging player. Of course, in your case, that won't matter.
One other note - and this is for everyone - if you happen to be the last one to take your turn, the host will generate a new turn immediately, and it's good form to stick around and play your new turn too. You'll see this happening from the network screen right after you upload. (Anyone who's played Dom2 with me knows I'm not exactly a golden example of this principle... but still...)
