Shares are said to be trading cum-rights as long as buyers will be entitled to a forthcoming rights issue....more on Cum-rights
With rights. 
Means with rights
With dividend; said of a stock whose buyer is eligible to receive a declared dividend. Stocks are us
The purchaser of a stock trading cum rights is entitled to buy shares of a new issue of stock in direct proportion to his or her existing holdings. 
When a company announces a rights issue, existing shareholders get the right to buy new shares,... <a target=_blank href='http://www.finance-glossary.com/terms/cum-rights.htm?id=1587&ginPtrCode=00000&PopupMode=false' title='Read full definition of cum rights'>more</a>
With rights. The owner of shares purchased cum rights is entitled to forthcoming, already-declared rights. The opposite of this is ex rights.