This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Rescuers
After Penny doesn't get adopted while other kids are, Rufus tries to comfort her with "Faith is a Bluebird". She is convinced of her own homeliness nevertheless, making it all the more devastating that a child her age could have such heavy self-image issues.
Take a close look at the room Penny's staying in during her time in Devil's Bayou. There is a poster on the wall with stick figures, depicting her with a mom and dad. Don't cry, don't cry..
Could either be her actual mom and dad (if she remembers them), or an imagined drawing of the parents she wishes she had. The latter is a bit less heart-wrenching, but not much.
What makes it even more heart-wrenching is that if you really squint, the figures in question bear a slight resemblance to Medusa and Snoops. Poor little Penny probably thought that those two were the closest thing she would ever get to actual parents.
The song "The Journey" during the beginning credits. Something about watching the bottle be tossed in the ocean as the music wells up dramatically, just emphasizes how helpless Penny must feel.
Penny's breakdown after she prays for someone to find her.
Penny: Please let someone find my bottle, there's a message in it. Because running away isn't working. Amen. [Addressing her bear] Don't worry, Teddy, we'll be... alright... [collapses into tears]
Thankfully, Bernard and Bianca have just made it to her room and can reassure her.