I have called the characteristic that characters travel into fictional worlds a passage into unreality: passage, that is, into the world of an instance of unreality. The stories and novels that provide the fictional worlds in act II of Improbable Fiction are such instances. Passage means here that someone, namely Arnold, travels into the worlds of these fictions, instances of unreality. (Obviously, the notion of traveling itself is a metaphorical notion, just as 'passage' is; but let's ignore that issue at this point.)
No such thing can happen in the real world, of course. You and I, real people, cannot travel into the world of a story. (Except in the trivial sense that we can read a story and then imagine the world of that story. But we won't simply find ourselves, physically, in a Victorian house in the middle of the 19th century, as Arnold does in the play.) So passage into the unreal is something that only fiction allows: a fictional character can travel from within his own fictional world into the world of a fiction-within-fiction. So does Arnold, only that he visits not just one, but actually three different fictional worlds, all of them constructed out of materials from his friends' works.
previous post). But that kind of continuity is comparatively weak. It's just a similarity in appearance and behavior. Mostly, they are simply the characters in those nested fictions, nothing else. They don't have any memories or experiences from the surrounding world, the world of the play proper. So for instance, Brevis, who is in act I a retired schoolteacher who writes musicals (that is, he's a composer of music) transforms into a solid doctor in the Victorian setting and then into a senior agent of some kind in the science fiction setting. In none of those he seems to have any memory of his schoolteacher personality. He's just reduced to being these fictional characters. In other words, he's not really Brevis at all. The most we can say is that he appears in various roles with Brevis' appearance and some (not all) of his personality attributes.
Arnold, on the other hand, remains the same person. Not only does he keep his memories and basic personality (and also his name) in all the fictional settings, he also considerably struggles to recognize that he is now within those fictional worlds at the beginning of act II. He is a person from the 'real' world (the world of the play) who has just traveled, inadvertently, into a fictional world, and he has to find out about that new situation first. He is, in that respect, in a similar situation as we, the audience, are. Of course, in contrast to us, the audience, Arnold doesn't just watch, he is involved in all kinds of interaction, and he's even suspected of murder at one point. Arnold, in a word, maintains a continuity of personality; none of the other characters does that. Even though he has traveled into fictional worlds, he still has the memories of the originating world, and he has to unlearn some behaviors from there. For instance, he needs to learn the names of the other characters inside their respective worlds. When he encounters Clem for the first time in the early twentieth century murder mystery, he learns that Clem is by no means Clem, but 'Jim'. (Clem has taken on the role of a detective inspector in the crime fiction world of one of the writers' works, and in that role he goes by the name 'Jim'.) So Arnold calls him 'Clem', is corrected, and henceforth calls him 'Jim'. No such adjustment goes on with any of the other characters. They appear to have never been anywhere else but in that world in which they currently are. They haven't come from the surrounding world (the world of the play).
I think that such continuity is a necessary condition for passage into an instance of unreality. What would happen if, in contrast to the actual way the play is written, Arnold would have had no continuity of memory, and personality? What if he, just as all the other characters, had fully transformed into a character of the Victorian story, the murder mystery, and the science fiction romp? In that case, what we would have witnessed in act II would have been much more abstracted from the events in act I. We would have seen a first act that featured some writers talking about their writings, and then a second version of those writings, now acted out by people resembling the actors in act I, but without connection to them. Thus one effect of Arnold's continuity of person is to connect: to bind act I and act II together more strongly, and also to draw us, the audience, deeper into the events. After all, he is in a way in the same situation as we are. Just as we, the audience, remember the content of act I, so does he. By providing a possibility to identify with him, the play makes it easier for us to engage imaginatively. Arnold is, so to speak, 'our man on stage'. He is closer to us than the other characters, because he has the same memories of previous events as we have (and the other characters seem not to have), and he has to make sense of what's going on, just as we have, too.
The continuity of personality in Arnold and our sense of plunging from the world of the play into the worlds of those fictions within that world are two sides of a medal. If there were no traveler such as Arnold, the only thing we could perceive would be a sequence of, first, a play in which stories are talked about, and second, a number of dramatic performances of something resembling those stories — and we would perceive that as an arrangement made by the playwright (or the director). It's rather similar to reading an introduction to a dialogue of Plato, say, where the introduction quotes extensively and summarizes the content of the dialogue, and then continuing to read that very dialogue which comes in the same volume, after the introduction. There is an external editor behind this constellation. Compare this to the scene in Sophie's World in which Plato himself appears in a video recording and gives his spectator introductory questions that lead into his philosophy (which is afterwards explained to Sophie in a written overview article).
Thus there wouldn't be passage at all if none of the characters had any continuity through the different worlds. There's nothing impossible about a play being constructed that way. But it wouldn't feature any sort of passage any more. Passage requires continuity in at least one character, continuity throughout the world of the fiction and the world of the fiction-within-fiction. It must be the same, continuous person in the originating world and the destination world. It's the same thing with passage in other forms. When people enter dream worlds in movies like Inception, they retain a good deal of their personality from the world outside the dream — including their plans, of course, for otherwise the plot of trying to steal something specific (such as vital business information) during the dream would not be feasible. Likewise, no timetravel story really would make sense unless the timetraveler is the same person in the destination world (that is, the world at some past or future time) as in the originating 'present' from which she started.
 Jostein Gaarder, Sophie's World. New York: FSG 2007, 77–78. There are more interesting instances of passage in that novel, but those are for another time.