It could also be a fanfic that takes place in an alternate universe. In this universe, the events of 4x23 didn't happen as they did in the show. Maybe Beckett didn't become a detective in the same way, and Castle meets her in a completely different situation. They then start to solve mysteries together in this new setting.
One possible plotline could be that the baby has some sort of special ability or is in some way connected to a mystery they have to solve. Maybe the baby's birth coincides with a strange series of events in the city, and Castle and Beckett have to use their skills to protect the baby and figure out what's going on.
One possible plotline could be that Castle, in his over - the - top way, proposes something like a wild undercover mission where they have to pretend to be a couple in a very improper situation to solve a case. Beckett is initially shocked but then realizes it might be the only way to catch the criminal.
Maybe they stumble upon a government conspiracy. The government wants to keep something hidden and they are seen as a threat, so they are made to disappear. It could also be related to a scientific experiment gone wrong. They are in the wrong place at the wrong time and get caught in an energy field that transports them to an unknown location, causing them to disappear from their normal world.
It might also be unique because of the way fans can explore the 'what - ifs'. For instance, what if a certain character had made a different decision in 4x23? Fanfic writers can play with these ideas. They can also add their own personal touches, such as introducing new side characters that interact with Castle and Beckett in ways that are different from the main show. This gives a fresh perspective on the Castle - Beckett dynamic.
Perhaps they are trying to protect their relationship from outside interference. For example, if there are people in Castle's publishing world or Beckett's police department who don't approve of their relationship, they could pretend to be separated to avoid any negative consequences. This would allow them to still be together in private while keeping up the appearance of being single in public. Also, it could be a way to test their relationship. They might want to see how they would fare on their own and if their feelings for each other are strong enough to withstand a period of 'separation'.
One possible reason could be that they are on a secret mission. Maybe they are trying to protect a key witness or important evidence from a powerful and dangerous criminal organization. In the world of fanfic, this could lead to them having to disappear to keep their whereabouts unknown.
There's also 'Beyond the Case'. This fanfic takes their story to new heights by adding some interesting plot twists outside of the normal case - solving scenarios. It shows how their relationship might develop in different, more challenging situations. It's a great read for fans who want something a bit more out of the ordinary.
A Castle and Beckett baby fanfic could be about their journey into parenthood. It might explore how they adjust to having a baby in their lives. For example, Castle could be super excited and start writing new stories inspired by his new family experience, while Beckett might be a bit more cautious and protective.
One great fanfic could be one that focuses on the emotional depth between Castle and Beckett during that episode. It might explore their unspoken feelings in more detail, adding more internal monologues for both characters.
Well, it could be that Beckett is in a parallel universe where he has a different life and he's in bed with another man. In this story, they could be discussing their different worlds and how they got there. Maybe Beckett is an undercover agent and he has to pretend to be in a relationship with this man, so they are in bed just to keep up the pretense for some important mission. It could also be a story about Beckett's past life where he had a relationship with a man that he's now rediscovering while in bed with him.