Can random events kill your last remaining crew member?
Solution 1:
Yes, crewmembers can be killed at any point, including in those types of encounters. There is no mercy for being the last crewmember, their life is just as much at risk as any others.
Generally I tend to avoid those enounters when a blue option isn't present, as the loss of a crewmember can be a pretty big setback in general, not just on your last crewmember.
Source: Personal Experience