Unpaid share capital is where none of the monies due for an allotment of shares which have been issued has been paid.
It is quite common in smaller companies for the share capital to be unpaid and remain due to the company indefinitely.
There is no requirement, unless specified in the company's memorandum and articles of association, for share capital to be paid up. The only exception to this is where a company is being dissolved. Although the shareholders might enjoy limited liability protection, their obligation to pay for the shares which have been issued to them is not diminished.
Unless there is a specific need to issue a large amount of shares on incorporation, it is generally a good idea to issue as few as possible (often just one). This ensures that the amount which a subscriber may be called on to pay in the event of dissolution is kept to a minimum.