Basic Trope: A character pretends to be in a long-distance relationship.
Straight: Bob is with his buddies when the subject of girlfriends comes up and the others all talk about theirs. Bob has been dateless for a long time, possibly ever, but doesn't want to admit it, so makes up "Marie" who lives in "Quebec." His buddies are dubious, but Bob mentions Marie every so often to reinforce the idea that he's able to interact with a woman.
Bob goes so far as to forge "evidence" that Marie exists; blurry pictures, letters postmarked in Quebec; he even uses his vacation time to go up to Canada to "visit Marie."
Bob is roped into a trip up to Quebec. "Hey, we can visit your girlfriend! Right?" He quickly hires a local escort or actress to play "Marie" and hurriedly put together a dossier for the role.
"I used to have a girlfriend named Marie who lived in Quebec, but we broke up a while ago, so I'm free to date."
Bob does have a girlfriend in Quebec, but there relationship is very casual.
Justified: Bob is desperate to hide his dateless loser status, and he knows none of the other guys have been to Quebec. Besides, if he ever does get a real girlfriend, he can "dump" Marie with no problem.
"Marie" is treated like a Bigfoot-esque urban legend; Bob's friends spend their time studying supposed "sightings" of her.
As Double Subverted, when someone notices a message from a French-speaking woman on Bob's answering machine, asking why she hasn't been picked up from the airport.
To everyone's surprise, "Marie" turns up. However, she's actually a fake playing Bob for money, who can't reveal her without exposing his own lies.
Bob lives in Toronto, so it's not surprising he has a girlfriend in Canada. However, that supposed girlfriend lives across the continent in Vancouver, no-one's ever met her and he doesn't have any pictures, making her a Girlfriend in Canada.
Averted: No one in the story pretends to have a relationship with an imaginary person—although there may be genuinely mistaken claims of relationship.
Enforced: "We want to underline just how much of a loser Bob is. Make him claim he has a Girlfriend in Canada."
Lampshaded: "I know how lame it sounds, but Marie just doesn't like having her picture taken."
Invoked: Bob's buddies start a conversation about their girlfriends in full knowledge that Bob is dateless, just to see what he'll do when it's his turn.
Exploited: Bob's Fair Weather Friend Charlie mentions Marie when both men meet a really attractive single woman, so she'll think Bob is taken.
Defied: "I'm not going to lie. I am between girlfriends. Now that you've made me say it, do any of you have single sisters?"
Discussed: "No, I've never seen a picture of Bob's girlfriend either. Odd, that."
Conversed: "I thought I might like Generic Sitcom, but they're being way too mean to Bob with this imaginary girlfriend Running Gag."
Deconstructed: Bob's imaginary girlfriend is just a symptom of much deeper psychological problems caused by his social maladjustment. Over time, he becomes more and more engrossed in his fantasy of a perfect relationship, until he loses the memory that Marie doesn't actually exist. Meanwhile, real women who might be interested in Bob are discouraged because they think he's taken.
Bob made up the Girlfriend in Canada as a joke, and is sticking to the story because he thinks it's funny that his friends still believe it.
Bob really does have a girlfriend in Canada, and his friends have even met her a few times. They keep claiming he's doing this just to wind him up.