Unissued capital is only a token restriction. When a company is incorporated a maximum number of shares is specified in the legal documentation. Most companies will make this an extremely large number so they never face that limitation. See here.
You wouldn't necessarily expect the stock price to change. The reason a company issues new stock is as a way to raise capital. Although new stock is issued, the cash raised by the sale becomes an Asset on the company's balance sheet. There's a good worked example in this Wikipedia article.
Following a rights issue the Liabilities of the company will increase to account for the increase in owner's equity, but the Assets will also increase by the same amount with the cash received.
Whether the stock price changes will depend upon what price the stock is issued at and on the market's opinions about the company's growth potential now it has new capital to invest. If the new stock is issued at the same price as the current market price, there's no particular reason to expect the share price to change. Again Wikipedia has more detail.
When new stock is issued it is usually offered to existing shareholders first, in proportion to their current holding. If the shareholder decides to purchase the new stock in full then their position won't be diluted. If they opt not to buy the new stock, they will now own a smaller percentage of the company as their stocks will make up a smaller part of the now larger number of shares.