You must have wondered, from time to time, what happened after the play (or book, or film) you were watching ended. Did the characters live happily ever after? Did they get their just deserts? Real life, after all, never just stops.

Tom Stoppard gave us what was happening offstage while the play went on elsewhere (in Rosencrantz and Guildenstern are Dead) but it takes a writer with Brien Friel’s fecund imagination to propose not just what happens to characters in one play but that a character from one play might run into a character from another quite different play (albeit one by the same author).

Here, 15 years on, in a rundown café, Andrei Prozorov, the brother of those three Chekhovian sisters (and husband of the ghastly Natasha), wanders in to find Sonya Serebryakova, niece of that old fool Uncle Vanya.

Of course, they don’t know that, and you don’t really need to as Friel fills you in on most of the salient points; this is, after all, a kind of homage to Chekhov. But it helps to remember that Sonya, now armed with a surreptitious bottle of vodka in her briefcase, used to be the sensible one and Andrei, now busking on the streets of Moscow for enough money to buy some cabbage soup at the café, started out, at least, as the life and soul of the party.

What remains the same is the way the characters are still searching for any thing other than what they are. So Frances Barber’s Sonya is all business and bustle, trying to convince herself, never mind the bank and the agriculture ministry, that things really are going to be all right.

Meanwhile, Niall Buggy’s Andrei has invented an entire alternative history to impress this stranger. We come across them on the second night they have met when he is having to admit to his inventions. For a moment, there is the merest suggestion of an intimacy that might develop into something more. But of course it was the vision of himself that had rather charmed Sonya so that, in owning up to the truth, he eventually destroys the tiny spark that might have grown into a flame.

Garry Hynes’s production, the final piece of the three-part Friel season in Edinburgh this year from the Gate Theatre in Dublin, is a study in sepia, a foil to Patrick Mason’s light, white The Yalta Game (both join Faith Healer in repertory until the end of the festival). Barber, newly cast for this run, is perhaps a little too skittish as yet, that deep, deep world-weariness just eluding her. But Buggy, all smiles and little ingratiating gestures, hovers just as neatly over the emptiness as the characters in The Yalta Game.

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