Ideas
I have experienced this bug today, so far I have removed mods folder and repaired game, I also evicted the sim and moved them back in as it was saved directly before the sim was abducted. As soon as the save loads and plays the sim is in the middle of being abducted still even after following all the above guidelines. I did have a couple of mods and cc originally but very minimal and definitely never any alien eyes so it can't be that, that's caused it. The sim wasn't enrolled in any Get To Work careers either which I thought odd, they were in Evergreen Harbor and doing a freelance crafter career.
I noticed in the original bug report it was reported on a Mac, I am a PC user.
I experienced the exact same issue yesterday two times. Deleted mods, repaired the game and same thing happened again. Lost 5 hours of gameplay in total (never ending saving screen). The game has been broken since Life & Death patches I wouldn't be surprised if it's a bug/glitch unrelated to mods.