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1] I bought a shirt that a lot of the buttons had come off of.
Is the above sentence fine? For me to write 'come off of' sounds odd.
I found the sentence in a website. He or she has translated the following French sentence into English in the above manner.
Coming off of buttons of your shirts is commonplace. However, to write those words at the end of a sentence sound odd to me.

J'ai acheté une chemise dont beaucoup des boutons s'étaient détachés
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I bought a shirt from which several buttons were missing.
I bought a shirt, and found several buttons [to be] missing.
I bought a shirt that was missing several buttons.

This is more common in my experience, unless you mean to imply that they were still loose in the package.
Comments  
Rotter1] I bought a shirt that a lot of the buttons had come off of.
This is not a grammatical sentence.
The problem is on the relative clause. You can use the same clause with a slight modification.
I bought a shirt which had a few buttons already come off.
Students: We have free audio pronunciation exercises.
"off of" is always nasty; "off" suffices. The sentence you quote is especially ugly, and can't be properly fixed simply by deleting "of". You could say "I bought a shirt that had lost a lot of buttons."
 Avangi's reply was promoted to an answer.
Thanks
The English sentence is not written by me.

It was written by a French language expert. He or she has translated it into English. I read it in French language website. As I thought it was awkward, I posted here.
Students: Are you brave enough to let our tutors analyse your pronunciation?
I bought a shirt that a lot of the buttons had come off of.
Is the above sentence fine? For me to write 'come off of' sounds odd.

I wouldn't condemn it as strongly as some have.
I'm sure I heard similar things hundreds of times in casual conversations growing up.

On the other hand, I wouldn't exactly call it "fine." Emotion: shake