let's said about the actual political implications despite the ASB-ness of the scenario, and let's say that Soviet Moon program is much more advanced than OTL, with them actually trying to beat the US on landing on the moon.
US landed first and stranded, Soviet cosmonauts, knowing the potential tragedy, proceed to land near the US Landing site , not the planned one, said "we come to help you, CYKA" while planting Soviet Flag near The American One, and despite the craft not built to hold that many people, managed to use Soviet ingenuity by throwing out many scientific modules and re-fitting Apollo's oxygen tank with duct tapes to make room for the astronauts all while they survived on what is basically starvation diet and copious amounts of vodka during the reentry.
The Rescue is a success, and US-Soviet relationship thawed to the point of mutual cooperation being possible. Cold War has been put on hold, and the word CYKA, ended up as an universal sign of friendship.