This topic is really hard, I think in Blood some situations like this happen because he's a vampire with heightened senses. Plus, the FL is a badass doctor that graduated from medical school at 17 or something like that. She's supposed to be a very gifted doctor, and is very high up at just 30 years old,
There's also My Amazing Boyfriend, he's an inmortal revived by her blood and they have a connection because of it. I think he can feel when she's in danger, can't remember how.
In Man to Man he's a secret spy and gives the FL a coin with which he can track her and save her. He has a lot of tech gadgets at his disposal a little bit more realistic than in healer.
In Mirror of the Witch he becomes her shield, literally like he is the actual mirror the title mentions. They have the unique connection that only him can shield her from the black magic.
In Legend of the Blue Sea they are present reincarnations of their past selves, the ML dreams what happened in the past and makes the connection that everything is basically repeating itself, so he's able to predict when she'll be in danger and save her (not always though).
This is all I can think of, I hope I helped. I'm interested in this theme now too.