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 their relationship is very casual.
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.
Exploited: Bob's Fair Weather Friend David mentions Marie when both men meet a really attractive single woman, so she'll think Bob is taken.
Defied: Bob tells the truth about his single status.
Discussed: "I'm not going to lie. I am between girlfriends. I was going to pretend I was in a long-distance relationship or something, but I decided against it. Now that you've made me say it, do any of you have single sisters?"
Conversed: "I thought I might like Generic Sitcom, but they're being way too mean to Bob with this imaginary girlfriend Running Gag."
Deconstructed: Real women who might be interested in Bob are discouraged because they think he's taken.
Reconstructed: Most single women don't believe Bob's story.
Played For Laughs: "Marie" shows up, but it's Bob in a Wig, Dress, Accent disguise. He fools almost no one, except Bob's rivalEthan, who tries to steal Marie from Bob before "Bob" returns.
Played For Drama: 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.
Untwisted: Bob makes up the Girlfriend in Canada as a joke, and only sticks to the story because he thinks it's funny that his friends believe it.