When share are loaned out by (A) to (B) who wants to short the shares, the actual shares are no longer in (A)'s account. There's a book entry indicating that (A) owns them (an IOU) but there is no longer any physical possession. (B) now sells the shares that he borrowed to (C) who now owns them and has physical possession.
No new shares have been created in this process. However, a new long position and a new short position have been created. So if this involved 100 shares, the end result would be that (A) owns 100 shares (IOU), (B) is short 100 shares and (C) owns 100 shares for a book entry total of +200 shares and -100 shares which equals +100 or the original amount of shares.
The brokers keep track of these transactions as well as borrow costs to be paid by (B) to (A) as well as any dividend paid from (B) to (A) if (B) is short the shares on the ex-dividend date while (C) gets the actual dividend).