Motionless Makeover

Putting silly things on people who, for one reason or another, are stuck in a particular pose.

The guards at Buckingham Palace, whose duty it is to never move, are common targets for this. However, people under the impression that TV Never Lies will be in pretty big trouble for actually trying this in Real Life.

When it hews closer to "they passed out so we drew on them", it's Face Doodling.

Examples of Motionless Makeover include:

Buckingham Palace Guard Examples

An episode of Mr. Bean involved him decorating the Buckingham Palace guards and doing funny poses with them
The second Austin Powers has a montage where he and Felicity goad a palace guard into participating in this.

Film

Os Trapalhões na Guerra dos Planetas (aka Brazilian Star Wars) has one of the protagonists, Didi, doing that to a paralyzed Darth Vader knockoff.

Live Action TV

Seen in the Christmas Episode of Community, "Comparative Religion" (although Troy is actually standing still so Abed can do this).
In a Christmas Episode of My Name Is Earl, the tradition in Ernie's Crab Shack is the first one to pass out drunk gets to be the Christmas tree.
On Wizards of Waverly Place, while Justin practices a time freeze spell, he puts a glass of water on Alex's head while she's frozen. This plan backfires as Justin falls to the ground, causing time to unfreeze and causing Alex to look down and having the glass fall on Justin.
On Salute Your Shorts, Ug is in a trance after his girlfriend dumped him. One of the campers puts a danish on his head.
In an early season seven episode of Buffy the Vampire Slayer, Dawn is paralyzed by a demon. Anya has fun posing her. When they have to run off to save the day, leaving Dawn sitting on the couch with her arm extended, Buffy comes back momentarily to stick a remote in Dawn's hand.
In Kenan and Kel, Kel does this to Kenan's parents once the two become so shocked that they freeze when they realize their expensive TV was replaced.

Newspaper Comics

In a Dilbert comic, Dogbert took advantage of Dilbert being in a "game trance" and stacked dishes on his head. He apparently did the same to Ratbert, who didn't notice, despite being conscious at the time.

Web Comics

Justin of El Goonish Shive likes doing this to Nanase when her body's unconscious during the use of her Fairy Doll spell. He limits himself to the hairdo, however.

Western Animation

In the Venture Brothers episode "O.R.B.", Hank and Dean cover Orpheus in toilet paper while he's astral projecting, which freezes his body.