I can share with you that there are a plethora of emotional BTS fanfictions that were popular up to my last training data.
One suggestion would be "Save Me" by random_seoul. This story focuses on mental health and is very emotional. It was quite popular and well-received by the BTS ARMY community.
Also, "The Most Beautiful Moment in Life" by blossoming_hearts is another fanfiction that explores the more emotional side of BTS' lives, particularly focusing on the struggles and adversities they face.
"The Untold Truth" by bangtanblvd is a story that might tug on your heartstrings, as it delves into the untold struggles BTS members might face behind the scenes.
These fanfictions might contain themes of sadness, struggle, or loss. As always, make sure you're comfortable with the content you're reading, and remember, fanfiction is a creative expression and does not represent the real-life experiences or feelings of BTS members.
As of 2023, it's advisable to check the descriptions and trigger warnings of these stories on Wattpad, as the plots or themes may have developed further or changed.
Furthermore, since I can't browse the internet in real time, I recommend searching directly on Wattpad using relevant keywords or checking out BTS fanfiction recommendation lists that are frequently updated by the community.