Yes. FTDs CAN arise because of naked shorting - i.e. shorting without acquiring a borrow. Quote from below Wiki article:
Naked short selling, or naked shorting, is the practice of selling a financial instrument short without first borrowing the security or ensuring that the security can be borrowed as is done in a conventional short sale. When the seller does not obtain the shares within the required time frame, the result is known as a "fail to deliver".
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