Alright. Risks.again. You need to make a choice. If you don't got enough raises to deal with all of it? You must choose what you want to do and what you want to have happen. It's a matter of : 1) have GM set up the Consequences of your actions. 2) roll the Dice Pool. 3) count raises. 4) choose what you want to accomplish. Maybe you can suffer a bit of damage if it means that you can get the letter? This part of the system is all a matter of judging risk management. There are people who don't use that all that much, and just want to have a damn skill check, but this is not how this game works. Running out of Raises is not a problem in Risks, because you always spend raises to deal with the basic Risk at first, and then see what Consequences you are willing to suffer and what Opportunities you are willing to take. In Dramatic Sequences it is a bit different, because there you are still a part of scene, and can freeform roleplay, but the GM has the final word of what happens to your character when you do stuff, where you can spend your Raises in a Dramatic Sequence to influence the story around you. If you run out of Raises in a Action Scene? Then your round has ended and if the same is the case with the other characters, then we're probably going to roll new Approaches and do the next Action rounds.

Ok, you're talking about the walkthrough Risk example on pgs 172 and 73, right?  I'm not sure what the confusion is.

The player rolls 3 raises.

The intent: "I want to cut down the chandelier and use the rope to climb down to safety.” (presumably out the window of the burning castle)

The Approach: Brawn+Athletics (trying to cut down the rope and use it to climb down the wall while dodging fire)

The Consequences: 2 wounds from the fire

The Opportunity: Secret blackmail papers

The Hero rolls and gets 3 Raises.  

1 raise achieves your intent: cut the rope and use it to get out of the room (a more persnickity GM might rule this is 2 actions and thus requires 2 raises, but that isn't the case in the example, so...)

That leaves you 2 raises to do other stuff.  You could avoid BOTH wounds, or take ONE wound and grab the letter, or take BOTH wounds, grab the letter, and do something else with your last Raise.

Don't worry about Death.  There's no villain in the room so your character cannot (technically) die.  But there is no telling where you'll come to when its all over.  Also, where do you get that getting out of the burning room alive takes 4 raises?  In the example, it's established that it only takes 3 at the most (assuming you are down to your last Wound and about to become Helpless).  Plus, you do NOT have to take the Opportunity.  That's the point of them, to make you think long and hard about how you spend your Raises.

The mistake you are making is the walking through the room and using the chandalier.  The INTENT in the example is to use the chandalier rope to get out of the room.  That's what costs a Raise.  The GM in this case is being charitable and not charging a Raise for each individual action.  Which is fine – this is a Risk, not an Action Sequence.  Plus, it's meant to be a simple explaination.

My character has only 2 Raises and is 1 wound away from being helpless/uncouncious. Since I therefore need a total of 3 Raises to get out I'm short 1 Raise. Even tho 'I'm not dying because there is no villain in the room', I'm still helpless/incouncious and alone in a flamming building.

The whole point of my question is: is there anything to do (other than hoping for a Deux ex machina from the GM) if you are in a situation where you do not have the bare minimum Raises to get out of the scene?

That depends on your definition of deux ex machina.  It's a feature built into the game.  Basically, if you run out of Raises, your fate lies in the GM's hands.  I can think of a lot of...unpleasant developments from this scenario that may players would not consider deux ex machina, as they do not favor them in the least.  Consider the genre we are talking about here.  Also remember that 7th Sea is not meant to be a simulationist game.  Those wounds have no real connection to any physical condition beyond Helpless.  A Dramatic Wound =/= a wicked cut unless the GM and/or player say so.

But let's assume the worst, okay?  They are a variety of ways you could play this out at the table:

• 1 Raise gets you out of the burning building, but you are helpless thereafter.  There are no consequences to going OVER 20 wounds.  Helpless is helpless.  There are no negative hp.  You crumble to the ground at the foot of the building, unconscious and unmoving.
• A hero point lets you act while helpless, so if 1 raise isn't enough spend as many hero points as you need to get out.
• Spend that 1 raise to have someone rescue you.  Who is it?  Why did they save you?  What do they want in return?
• You are out, but not the rest of the group.  Can one of them save you?  You spend your raise to grab the letter.
• You spend your last raise: the floor falls apart beneath you, dumping you into s safe place in the cellar.

Now as far as deux es machina goes:

• You wake up bandaged from head to toe in the hospital.  The surgeon believes you are someone else, and one of his aids plans to kill you in your vulnerable state.
• You wake up in the bed of a old lover, an assassin of considerable skill whose only weakness is you.
• You wake up chained in a cell by the villain you were hunting.
• You wake up in bed to find you have been rescued by an unknown villain who wants something in return.
• A deivas/djinn/fey offers to save you, just say the word.
• So THAT'S what that syrneth artifact does!!!  But there's a catch!
• As your vision fades, you see an old rival standing above you.  He says, "not this way.  You will not be spared my revenge so easily."

 

The way to get out of that situation is ultimately how creative you and the GM are cool with each other being. 
You could create an oppurtunity to break a window, or that the window lock is open already and you just need to push it open, then climb out without being burned. Maybe the tapestry on the wall is just thick enough and you take that, wrap it around yourself with the letter in hand and then walk/run out of the room?

Spend a hero point to ignore wound conditions for a round as well.