What happens If I remove an apple ID from one of my iPhones?

My mom has 2 iPhone with the same Apple ID, she wants to remove her apple Id from one of them but she's afraid that her data may be lost on her other one.

No, her data will not be removed from the phone. If it does, it will usually ask you if you want to keep some data (like Notes) on the phone.

However, after she does this, the phone will no longer sync with each other.

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