> Someone loans out 10 shares to a short who then sells them to someone else. All of a sudden there are 110 shares out there.

No there isn't - there are 100 shares total at all times, and every time those 10 shares you mention change hands, the cap table is updated (or should be) to reflect this. First they are owned by the original owner. Then they are owned by the shorter (and a contract is in place to return the same amount of shares and any dividends to the original owner). Then they are owned by the person the shorter sells to. At no point are shares duplicated.