She might be too big compared to the size of the doggy door. Maybe she was trying to reach something on the other side in a hurry and didn't realize she wouldn't fit.
If the doggy door is removable, they could take it off completely. This would be the quickest way to free her. However, this might require some tools depending on how the doggy door is attached. Once it's removed, she can simply step out or be lifted out easily. Also, while trying to get her unstuck, it's important to keep her calm so she doesn't struggle too much and make the situation worse.
Another situation might be that there was some kind of malfunction with the doggy door. She might have been leaning against it while it was in an open or half - open state, and then it closed on her, trapping her in an embarrassing position.
One possible outcome could be that she gets rescued by someone nearby. Maybe a neighbor hears her cries for help and manages to free her from the doggy door.
One possible plot could be that Allen is a curious character who was exploring an old haunted house. His tiki ghost hand, which has a mind of its own, reaches out to touch an ancient door. As it tries to pass through the door, it gets stuck. Allen then has to figure out a way to free it, perhaps by using some magic spells he learned from a local witch.
Perhaps in the fanfiction, the Tiki hand getting stuck is a sign of some sort of magic at work. Maybe the door is enchanted, and the only way to free the hand is to solve a riddle or perform a specific task. This could lead to an adventure for Allen as he tries to figure out how to free his hand.
Maybe Allen will feel a sharp pain at first. Then he might start to panic and try to pull his tiki hand out. If he can't do it by himself, he'll probably call for help. Someone might come and try to carefully free his hand without causing more damage.
Well, Allen might try to pull the hand out forcefully. But this could have unexpected consequences like the door breaking open and releasing a horde of mini - ghosts. Then he'd have to deal with them while still trying to free his hand.