Let's take Walmart. In 2013, Walmart had assets valued about 200 billion United States dollars. Let's define a walton as a fixed one-quadrillionth (10-12) share of Walmart. If the number of waltons is fixed permanently at one quadrillion, then a walton will always represent 10-12 times the assets of Walmart. Thus a walton would be worth one 10-12 times 200 billion USD, or 0.0002 USD.
Let's say that the value of Walmart's assets rises, due to acquisition of resources and/or the devaluation of the dollar, to 250 billion USD. Then, if Walmart never issues more waltons, the value of the walton compared to the USD will rise to 0.00025 USD.
The theory behind this is that a corporation could pay its employees in shares of itself, and accept its shares as currency for purchase. For example, let's say that a gallon of milk costs $5 and Walmart is valued at 200B USD. Then Walmart could charge 25,000 waltons for that gallon of milk. Another example: Let's say that a Walmart employee makes 10 USD per hour and works 30 hours a week. Walmart would owe that employee $300 for that work, but could pay them 1.5 million waltons.