That means she was probably last seen or heard from that afternoon a few hours before the sub launched.
Edit: Here: http://ekstrabladet.dk/112/kim-isabel-forsvundet-i-ubaadsdra...
Also, the eyewitness accounts of the sinking make it sound like the sinking was deliberate:
"Kristian Isbak, who had responded to the Navy's call to help locate the ship on Friday, told The Associated Press he first spotted Madsen standing wearing his trademark military fatigues in the submarine's tower while it was still afloat. "He then climbed down inside the submarine and there was then some kind of air flow coming up and the submarine started to sink," Isbak said. "(He) came up again and stayed in the tower until water came into it" before swimming to a nearby boat as the submarine sank, he added." [3]
[1] https://www.reuters.com/article/us-denmark-submarine-idUSKBN...
[2] https://news.ycombinator.com/item?id=15000076
[3] http://time.com/4898129/submarine-owner-detained-over-journa...
His girlfriend disappears in a normal manner, well, normal for a disappearance, he disappears in outlandish style in a sub sinking, he was going to swim to a pre-prepped dinghy or some quiet boat anchored nearby and disappear from history (perhaps with a pile of money?) but whoopsie a passing boater not part of the plan at all, coincidentally saw him and "helped" him out by declaring an emergency and fishing him out... So much for that tragic disappearance and drowning and missing body.
Now she's disappeared successfully on some tropical island retired wondering when he's gonna get there, or wondering if she should keep all the money (assuming any has disappeared at all, of course) or if she should come forward.
The whole thing sounding like a hollywood movie plot means my speculation sounding like a movie plot isn't necessarily disqualifying.
Its also worth pointing out that this is a "submarine story" only in the sense that the Reiser murder trial was about linux filesystem development.
There is a photo floating around that might be Kim Wall in the tower of the submarine o̶n̶ ̶F̶r̶i̶d̶a̶y̶,̶ ̶d̶u̶r̶i̶n̶g̶ ̶d̶a̶y̶l̶i̶g̶h̶t̶ ̶h̶o̶u̶r̶s̶.̶.̶.̶w̶h̶i̶c̶h̶ ̶w̶o̶u̶l̶d̶ ̶b̶e̶ ̶o̶d̶d̶.̶[1,2] That doesn't imply girlfriend though. Could also be that the "Friday" was a mistake and the picture is from Thursday.
[1] https://www.reuters.com/article/us-denmark-submarine-idUSKBN...
[2] http://www.skd.se/2017/08/12/madsen-nekas-forklara-sig-infor...
Edit: Photo was from Thursday, not Friday. Apparently the Reuters caption is wrong. http://www.zoox.se/submarine-inventor-charged-with-murder-of...
The FBI has some data on circumstances/motives here: https://ucr.fbi.gov/crime-in-the-u.s/2010/crime-in-the-u.s.-... You can pretty quickly find a few that might be plausible.