ABC News found a female stray in the Kievskaya station, and barely managed to follow her as she zipped between the legs of the bustling travelers around her to catch a ride on the Koltsevaya Line.
Once on board, she settled down on the floor among the feet and legs, even dozed a bit, and occasionally got up for a brief conversation with a friendly human.
I maintain the perspective that animals – not just dogs and cats – are smarter than we give them credit for.
See this older (2010) article: Russia: Stray Dogs Master Complex Moscow Subway System – ABC News
And this newer one: Stray Dogs Commute to Work by Subway
Thanks to this Reddit thread.