In some fanfictions, the hug could be a result of a mind - control or possession situation. The Earl might have taken over Allen in some way and the hug is a way to show his dominance over Allen's body. Or, on the other hand, it could be a moment of weakness for the Earl. Maybe he sees something in Allen that reminds him of his own past or a part of himself he has lost. And this realization leads to the hug as an impulsive act of connection, which then sets off a chain of events that completely changes the dynamic between the two characters in the fanfiction world.
Perhaps in the fanfiction, the Earl and Allen have a moment of understanding. The hug could be a sign of a truce, even if it's temporary. It could be that they both realize they have more in common than they thought, like their connection to the Innocence in some unexpected way. And this hug is a physical manifestation of that new - found understanding. However, it's also likely that the hug is a part of a more complex emotional battle between them. The Earl might be using the hug to taunt Allen, reminding him of his own inner turmoil and the difficult path he has to walk as an Exorcist.
The plot might also be that the Earl's hug is a way to get Allen on his side. He could be trying to convince Allen that there is a different path than the one he's currently on, and this hug is the first step in that persuasion.
There could be many interpretations in such a fanfiction. Maybe the Earl has some complex motives behind hugging Allen. It could be a moment of false kindness, where he's trying to manipulate Allen in some way, perhaps by making Allen lower his guard.
Perhaps a plotline could center around the Innocence within them reacting to the pregnancy. Maybe Lenalee's Innocence has some sort of special reaction, like providing an extra layer of protection. And Allen could have dreams or visions related to the future of their child, which could lead them on a new quest to understand what it all means in the context of the D.Gray - man world.
Perhaps the Earl discovers Allen when he is in a vulnerable state. The fanfic might explore how the Earl's presence affects Allen's development. It could also show Allen's internal struggle between the kindness the Earl might show him and his loyalty to the Black Order. It could be a story full of psychological drama as Allen tries to figure out the Earl's true intentions.
Isolation is also a theme. Allen is often alone in his struggles, being the host of the 14th Noah. Fanfics may depict his feelings of isolation from both the Exorcist side and the Noah side, and how he copes with being different from everyone else.
You can try looking on fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. There are often a lot of D Gray - Man fanfictions on these platforms. Just use the search function and type in relevant keywords like 'D Gray - Man', 'the Earl', and 'Allen' along with 'hugging' to narrow down the search results.
There are some fanfics that focus on Allen Earl's growth in power. They might describe his training sessions in more detail, and how he overcomes his weaknesses. Maybe he discovers a new form of Innocence or a unique way to use his existing powers. These fanfics often add exciting new elements to his character development.
Maybe the Earl hides Allen in a parallel dimension where time moves differently. Allen has to find a way to get back to his own world while also dealing with the strange rules and creatures in this new dimension. The Earl's motives for doing this could be to keep Allen away from the Order and use his power for his own evil plans later.
There could be. 'D.Gray - Man' has a large and dedicated fan base, and fanfiction writers often like to take the story in unexpected directions. The idea of Allen dying is a rather dark and dramatic twist that some writers might be interested in exploring. You can start your search on popular fanfiction websites like Archive of Our Own or FanFiction.net.
Fanfiction.net could also be a good place to look. However, the organization of the stories there might not be as neat as on AO3. But still, it has a vast collection. Go to the site, use the search function and type in the relevant keywords to find the fanfic you're interested in.