Non-Renounceable Rights

What Does Non-Renounceable Rights Mean?
An offer issued by a corporation to shareholders to purchase more shares of the corporation (usually at a discount). Unlike a renounceable right, a non-renounceable right is not transferable, and therefore cannot be bought or sold.  

Investopedia explains Non-Renounceable Rights
Issuing more shares dilutes the value of outstanding stock. But because the rights issue allows the existing shareholders to buy the newly issued stock at a discount, they are compensated for the impending share dilution - the compensation the rights issue gives them  is equivalent to the cost of share dilution. However, shareholders who do not take exercise the rights by buying the discounted stock will lose money as their existing holdings will suffer from the dilution.