If someone on the ISS had a medical emergency that required them to immediately return to earth (such as a severe stroke - something where they could not give them ideal care on the ISS and required urgent care), and it was not during a normal crew rotation (and there was not a launch planned in the next week or two), would all of the residents of the space station be evacuated (particularly, assuming there were only the one lifeboat, and not a spare)? Or would one or more of the astronauts/cosmonauts/etc. remain on board (despite the lifeboat leaving the station)?
All of the crewmembers assigned to the sick crewmember's crew transport vehicle (which as of this writing means the Soyuz) would have to leave as well. Otherwise they would be left without a means of escape in the event of a station emergency.
For a six person crew, with three crewmembers assigned to each Soyuz, three would have to leave.
For the current situation (February 2020), with only three crewmembers aboard, the station would be left un-crewed. A most un-desirable situation, but budget realities and the slips in Commercial Crew vehicle availability have put the program there.
References (sorry, Quora answers, but NASA does not publish ISS Flight Rules, and I used to work with both of the guys that wrote these answers, so I can vouch for them being JSC employees)
1$\begingroup$ Thanks for the quick answer! Is there any documentation of this, or is this just "common knowledge"? $\endgroup$– JoeFeb 12, 2020 at 19:34
4$\begingroup$ It's probably in the ISS flight rules, but NASA has not made them public. quora.com/Are-NASAs-ISS-full-flight-rules-available-publicly $\endgroup$ Feb 12, 2020 at 19:34
5$\begingroup$ @Mark the custom seat liners are removable - the STS-135 crew brought theirs up w/ them on the shuttle. That doesn't make staying up there w/o an escape vehicle a good idea though. $\endgroup$ Feb 13, 2020 at 3:49
7$\begingroup$ So if an accident results in serious injuries to two crewmembers from different Soyuzes, does everyone have to leave, or is it possible for someone to use a Soyuz seat that isn't theirs? $\endgroup$– Nick SFeb 13, 2020 at 15:28
3$\begingroup$ @NickS Based on the comment above yours from Organic Marble I would guess they could swap these "custom seat liners" but everything I know about it I learned from this question. :) That would be a good question to post. $\endgroup$ Feb 13, 2020 at 20:31