Well, the answer appears to be very complicated, but, as grass is a perennial, it sounds to be no more complicated than the answer for any other perennial. However, as it is a perennial, it essentially sheds and regenerates on its own. It is amazing now that I think about it. How many other forms of life in this world simultaneously die and rebuild themselves?
Grass has rhizomes which are underground root systems that keep growing and sprouting horizontally:
(from link below)
Apparently plants that have rhizomes live a very long time:
Hardier perennials might return year after year for 20 years or more. Perennials have structures, such as bulbs and rhizomes, that allow them to survive for many years.
Also interesting is that plants have a crown. Technically, the crown is everything above the roots. However, as far as grass goes, the crown seems to be often referred to as just the little white part right above the roots. This is the most important part of grass. Your lawn may look dead, but the only thing that truly matters is the crown. If the crown is hydrated then it can always grow more leaves and the crown requires much less water than its leaves (the green part).
If you have a water restriction or limited access to water and your lawn appears to be dying, the only thing that you need to focus on is hydrating the crowns and, based on this article, it only needs a quarter of what the leaves require:
Healthy green grass uses about one inch of water each week. However, when your turf is brown, it uses much less. In fact, you only need to apply about one quarter of an inch per week (or about a half inch every other week) to keep the crowns hydrated, and ensure that your grass will green up when the rain begins. It is not a good idea to apply much more than this amount, as the turf will start to send out new green leaves which will require lots of water to maintain their greenness. Water at night or early morning, when peak demand is lowest, and evaporative losses are least likely.
While looking for these answers, I ran into several other words that seemed interesting.
“Adventitious” roots grow off the stem rather than well under the surface like a traditional plant, where the primary root system is very shallow and the adventitious roots are responsible for anchoring (and feeding?) the plant. In this case, the stem is referred to as a stolon. Mangroves and palm trees are like this. Maybe any plant that flourishes in sandy or very wet areas?
Interestingly, maize (an obscure but import type of corn to Americans, for those that did not know) has adventitious roots:
More on grass growth and extension:
More information on adventitious roots: