Would a point come were sections of the walls would be knocked down and rebuilt further out or would new suburbs and such be left defenseless?
In the case of Rome, they would just build a new, larger wall around the city. It is important to note that city walls were huge undertakings that were extremely costly, so usually walls were only built when it was believed that the cost of not building a wall would exceed the cost of building one. By the time gunpowder was popular, city walls had generally ceased to be effective enough to merit the investment in their construction.
As a piggyback question: in the novel A Clash of Kings, by George R. R. Martin, a character orders sprawl around the wall to be burned down, so enemy soldiers can't climb it and get over the wall.
Was this ever a concern during a siege? Were walls ever climbed by enemy armies?
Many times they'd just be built around and/or knocked down.
Siena still has its walls up and fully intact due to post bubonic plague demographics, where the city didn't regain its pre-plague population level until the 1800s
Here's a picture of a fully modern city still surrounded by walls, and they still close the gates every night
http://www.kingtrips.net/italy/graphics/italy/map-siena-02-1600x1850.jpg
For one thing, sprawl didn't exist in the way it does today. True sprawl, like we see today in America, wasn't possible without motorized transport.
However, when the city started to expand beyond historic walls, in some cases it just became a matter of money. In medieval Dublin, living within the wall came with certain taxes. In return, those people obviously got the protection of the city defenses. Those who didn't want or couldn't afford the tax had to risk living outside the wall, and the city didn't have to responsibility to give them much protection. The fixation line of the wall still exists in Dublin between the area around St. Patrick's cathedral and the Liberties neighborhood across the street.
In the Netherlands, the growth of cities was severely restricted by their walls. (For a typical example of how those walls looked, see the city of Brielle. The suburb to the south is twentiest-century.)
The problem with suburbs and urban sprawl is not so much that they are undefended, but rather that they stand in the way of your cannons, making any construction directly outside the city walls impossible. Thus, you have to build the walls first, as in the case of Amsterdam mentioned above.
Most cities in the Netherlands kept their walls into the second half of the nineteenth century[1]; by that time, most Dutch cities were very, very crowded.
Look at the city of Utrecht, which took down its walls very early, in 1830: compare this map of 1865 with [this one of 1649](http://commons.wikimedia.org/wiki/File:Traiectum_-Wttecht-Utrecht(Atlas_van_Loon).jpg). In 1865, the city is still not much larger than in 1649, while having almost twice the inhabitants[2].
A very nice book on overpopulation in Dutch cities in the nineteenth century is Koninkrijk vol sloppen, but it is in Dutch.
[1] The fortress law of 1874 listed a large number of cities that were finally allowed to demolish their walls and was the end of the paradigm of defensible cities (with one exception). Most walls were turned into much-needed public parks, so that the form of the old fortifications can often still be recognised today.
[2] According to [this table on wikipedia](http://nl.wikipedia.org/wiki/Utrecht_(stad)#Bevolkingsontwikkeling).
