Done, interestingly, with a lot of rope and a large cloth gag for visual effect, on a young girl about 7, in a movie made by a summer camp, The Mystery of the Missing Jewels. It's obvious she isn't really tied or gagged especially tightly, and it's just for show, but that sure is an almost cartoonish amount of rope. Occurs at 14:47 in (link will skip you there).
Also done in an unusual way to a girl who looks about 10, in the independent film Caitlyn. She's tied to a pole (in part 2) with what appear to be metal strips pulled tightly. She's forced to make a Sadistic Choice between her freedom, or her parents' lives. Part 1Part 2
Knot Me. The premise of this short film? "What do you do when you wake up to find yourself tied to a chair?" Find out here. Yes, a short film literally about a young woman being tied up.
Happens to every one of the 5 middle-school aged heroes (of both sexes) in the independent kid-made film Bradley's Summer, which can be found on YouTube. Not only that, Bradley himself gets tied up while invisible. Yup, an invisible boy tied up with ropes that look like they're hanging in mid-air.
Happens to the two female leads in the independent film Green Eyed Monsters. They pretty much spend 80% of the movie tied up. Strong language warning on this one. It's certainly not made by kids.
Five actresses have it happen to them in Blackout. From the same director. Hmmm...
Linkara has been tied up twice, once by Sage and the other time by Mechakara. The former had a gag involved.
The Nostalgia Critic was held hostage by the Game Heroes and was tied up with a bag over his head. The bag's pulled off at the start, but he's still squirming and getting manhandled throughout the promo. Later on, Hyper Boner like tying him up with pink handcuffs and chains.
The Chick stunned Spoony in the face, tied him up with extension cord and gagged him with a sock at the start of their Dune IRiff. She's also kidnapped and tied up Todd in the Shadows at least five times. note Add on her chloroforming of the Critic and you start to get a good reason why the fangirls love her.
In "Golden Book Video Killers XVI", Grumpy and Daffy were covering the Golden Book Video versions of The Bible stories, Noah's Ark, David and Goliath, and Jonah. Grumpy feared that Daffy would make crude and offensive jokes about the stories (since they were all about Christianity), so he tied up Daffy to prevent that from happening.
In the latest episode "Golden Book Video Killers - Si And Am's Edition", Si and Am (from Lady and the Tramp) do this to Grumpy in an attempt to sabotage the 5th anniversary of the show. Fortunately for Grumpy, Zeke Wolf showed up and was able to save him, which led to Grumpy confronting the two mischievous cats about it near the end of the episode.
In Entry #35, Alex and Jay manage to unmask the masked man after they overpower him and tie him up, revealing his identity for the first time. It's Tim.
In Entry #67, the hooded figure knocks out Alex with a pipe at the abandoned hospital and then ties him up to a chair. He allows Tim to practically knock his lights out before he takes Alex's gun and nearly finishes him off himself. Fortunately for Alex, the Operator shows up just in time to save him.