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Astronauts are now stuck on International Space Station indefinitely due to issue with Boeing Starliner
(www.independent.co.uk)
Also docked to the space station is SpaceX’s Crew Dragon capsule that ferried four astronauts to the ISS in March, and a Russian Soyuz capsule that delivered three others in September. Stich acknowledged that at least one of those vehicles could provide an alternative ride home for Wilmore and Williams.
Pretty sure Soyuz can be sent up empty if needed
It can, they did it last year, but generally any empty seats going to or from the station represent a big waste.
You'd have to convince russia to cancel a crewed mission to free up a spacecraft for that.
I'd put money on the upcoming august Crew-9 flight of a Crew Dragon to become the rescue craft. It's scheduled to have four crew fly to the ISS for a six-month mission, but I think NASA would probably fly it up with just the commander and pilot, and let the two "stranded" astronauts fill the roles of the two mission specialists for the full mission length. This would also give NASA, Boeing, and SpaceX time to figure out a way to connect Starliner pressure suits to Crew Dragon power/data/life support systems, and fly up that adapter hardware on a cargo flight.
The Crew Dragon is theoretically capable of flying seven crew, but that seat configuration has never actually been used on any orbital flights, and there's no way in hell NASA authorizes a major modification to a crew vehicle just weeks before it's due to launch.
Interestingly enough, if the two Crew-9 mission specialists are bumped off the flight, there are geopolitical-tension consequences. One of the mission specialists is Russian. NASA and Roscosmos have miraculously maintained a cordial working relationship despite waves hands around in general.
Most likely they'll come back in the boeing ship eventually, but if they have to be rescued, it'll be a significant money and time cost to whoever does it. I don't think russia is looking to do a huge favor for america that probably wouldn't be returned.
NASA Administrator is a high-prestige, high-profile political appointment. The Administrator answers only to the US President. There is never going to be a situation in the current political climate where a sitting President (regardless of party) asks for Russian help when there's another American company that's already successfully doing passenger taxi service to the ISS.
That puts the Roscosmos Administrator in an interesting political situation. There's probably going to be an internal political argument about how to respond. They could cheekily offer a certain-to-be-rejected offer of a rescue flight, but would be a domestic propaganda win. Or they could keep it professional with some variation of "We have trust in our skilled partners at NASA to resolve the situation".
I'd bet the latter wins out though. Roscosmos (and its predecessor organization in the USSR) and NASA have always kept a friendly and professional relationship, regardless of geoplitical tensions. The predecessor to the current Roscosmos Administrator was known for running his mouth off but the current one is a lot more professional and diplomatic.