In all vessel encounters there is the stand-on vessel and the give-way vessel. If In Extremis is reached because the give-way vessel is not doing what is required, the stand on vessel has a duty not to continue holding course and speed, but to take some action.
As the court has said, "There is no right of way on which a vessel is entitled to insist when it is obvious that it will result in danger of collision." The term comes from the use of the "last illness" or "dying declaration" which is final.
-A Riverman's Lexicon by Charles F. Lehman. p223