Why is space important in Middleton and Rowley's The Changeling?

First of all, it's definitely safe to say that space is one of the play's key themes. We see it in lots of different ways - but in the broadest sense, you should notice how the play moves from a wide open space (the port, gateway to the world, in the first scene) to a completely enclosed one (the closet in which DeFlores and Beatrice are shut by the final scene). Middleton and Rowley (though note that we can assume Middleton wrote the main plot and Rowley the sub-plot) can be seen to be using this tightening of the represented space to increase dramatic tension: as the audience senses the space becoming smaller, we understand that there is a movement towards something - and probably not something good! It's also definitely worth mentioning the sub-plot - set in the asylum - in response to a question of this kind. I'd encourage you to think about the effect on an audience of seeing the 'patients' being restrained: are Middleton and Rowley not then associating enclosure with madness? It would be hard not to associate the sub-plot with DeFlores and Beatrice's final scene - B earlier talks about "love's tame [we might say tamed!] madness". Finally, you should definitely always consider the effect of the offstage space: an audience fears what it can't see (Vermandero: "our citadles are plac'd conspicuous on promonts' tops/ But within are secrets"), and we associate it - as M&R clearly demonstrate in the final scene - with death, and sometimes the occult.
Going back to Greek theatre, dead bodies will often appear out of the skene, and when a character goes offstage near the end of the play, there's a high chance it's because they're going to die (characters are almost never killed onstage - you could quote Aristotle's Poetics on this one). You could also really usefully link to plays which feature other dramatic malcontents: such as Shakespeare's Hamlet (you could look at the 'curtain' scene in which Hamlet accidentally kills Polonius) or other Renaissance dramas like Kyd's Spanish Tragedy or Marston's usefully named The Malcontent. All of these plays should be understood in the context of what Stephen Greenblatt calls "self-fashioning": basically, a realisation during the Renaissance that each person was an individual and therefore free to make their own destiny. You could argue that Middleton and Rowley closing down of space is a rejection of the idea that we are free to make our own lives: DF and B - who have deviated from the norms of society - are trapped by the play's end. But how does DeFlores' taking matters into his own hands, killing himself and Beatrice, complicate this fact? There's lots to think about here! As ever, making sure you are keeping with the assessment objectives when writing out an answer.