The family visits their/a cabin in the woods. The kids see a local who tells them about the monster residing in the woods. It proceeds with them spotting weird things, indicators that there is indeed a monster.
Sun sets and the monster is real, it's pursuing the kids as they rush back to the cabin but the monster catches up and simply hands over a jacket, left behind by the son at the lake.
I do remember distinctively that as a ten year old I found the language employed very good and the build up was excellent.
I remember that the monster was called The Watcher/The Sentinel but do not remember exactly. Searching those two terms haven't yielded anything worthwhile as there are countless number of horror stories titled The Watcher.
I chose this story for a storytelling competition in 2013 (that means I was 13 years old back then not ten).
I may have given the impression that it was a kid's story, it is not.
All of this was before the era of creepypastas.