assistant: Dear [Name],

I’m so sorry about my thoughtless negligence and I apologize unconditionally for my failure by losing your [item].  I have caused you needless hurt by my carelessness, and I deeply regret my actions.  You trusted me with your possession and I broke your trust.   I have considered how instead of paying attention and being diligent in safeguarding your goods, I let you down through my own absent-mindedness.  That was wrong of me, and it’s inexcusable.  I wish to replace the item to atone for my shortcoming to prove I am coming from a position of genuine remorse and goodwill.  Moving forward, I promise to be respectful to you and what is precious to you.  You mean so much to me as a friend and I never would wish to lose something important to you, and our friendship means everything to me. I would love to pick up this matter when we see each other again so I can make things right.

prompter: The language is overly formal and flowery. Make it more sincere and less repetitive.

assistant: > Dear [Name],
> 
> I am so sorry for losing your [item]. I know it was a prized possession of yours and I feel terrible for causing you any pain or inconvenience. My negligence and carelessness have led to this situation, and I fully take responsibility for my actions. I can only imagine how disappointed you must feel, and I want to make things right.
> 
> I realize that no amount of apologies can replace the value of the item, but I promise to do my best to make it up to you. Whether it is by finding a replacement or compensating you in some other way, I will make sure that you are not left empty-handed. Please let me know what I can do to make things right.
> 
> I value our friendship deeply, and I am ashamed that I let you down in this way. I promise to be more mindful and responsible in the future, especially when it comes to things that are important to you. You can trust me to be more careful and diligent in the future.
> 
> Once again, I am truly sorry for losing your [item]. Please forgive me, and I hope that we can move past this and continue to strengthen our friendship.

Here is an apology which is more sincere and less repetitive. Perhaps you could tell me more about your situation so that I can make the apology more specific and personalized?

assistant: Dear [Name],

I'm so sorry for losing your [item]. I know how much it meant to you and I feel terrible for letting you down. My carelessness was inexcusable and I want to apologize from the bottom of my heart.
I understand that this must have caused you a lot of pain and inconvenience, and I want to do everything I can to make it right. I would like to replace the item as a gesture of my sincere regret and to show you that I am committed to making things better.
I value our friendship deeply and I never want to do anything to jeopardize it. Losing your [item] was a huge mistake and I promise to be more careful and respectful of your belongings in the future. I hope that we can put this behind us and move forward.
Once again, I am truly sorry for what happened and I hope that you can find it in your heart to forgive me. Please let me know if there's anything else I can do to make things right.

assistant: Dear [Name], I am truly sorry for having lost something that was clearly very important to both you and the friend who gave it to you. I know I can’t really make it up to you, as some things are irreplaceable, but hope you can still find it in your heart to forgive me.