Well, another place could be Tumblr. There are many D Gray - Man fans on Tumblr who might post or recommend such fanfictions. You can search through the D Gray - Man tags and also look for fanfiction - specific tags. However, the Tumblr search can be a bit tricky sometimes, so you might have to dig a bit deeper. Also, some D Gray - Man fan communities on Reddit could potentially be a source. You can post a request there asking if anyone knows of any fanfictions with this specific scenario.
Finding specific fanfiction can be a bit of a hunt. Some smaller, more niche fanfiction archives dedicated to D Gray - Man might also have what you're looking for. You could try reaching out to D Gray - Man fan groups on Facebook or other social media platforms. Ask if anyone has read or written a fanfiction about the Earl hugging Allen. Additionally, check out some of the D Gray - Man fan - made blogs or websites. They might have links to or host such fanfictions themselves.
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 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.
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 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.
Another option is to check out some D Gray Man - focused fan communities on social media platforms like Reddit or Tumblr. Sometimes fans will share their own fanfictions or recommend ones they've read. You can also post a request asking for Allen and Road fanfictions, and chances are, some friendly fans will point you in the right direction.
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.
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.
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.
FanFiction.net is a great place to start. There are tons of D Gray - Man fanfictions there. Just search for the relevant tags and keywords.
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.
You can try fanfiction websites like Archive of Our Own (AO3). There are a lot of fan - created works there. Just search for 'D Gray - Man Chibi Allen' and you'll likely find some interesting fanfiction.