Most, but far from all, companies maintain a relatively steady debt load. When a bond matures, they fund its principal payout with a new bond.
Sometimes companies do take on more and more debt, meaning that CDS protection sold during earlier times of small debt loads becomes more valuable (and underpriced, from the point of view of the protection seller). Each increase in debt load is effectively a change in capital structure, which is an important and under-modeled part of quantitative finance.
Homeowners insurance runs some similar risks. A homeowner might significantly increase the value of his or her possessions while remaining under the same policy.
I originally thought you were asking about a key difference between CDS and fire insurance. Namely, there is not much risk of many homes burning all at once (modulo the occasional wildfire in the western USA). Corporate bankruptcy, in contrast, tends to happen in bunches.
The lack of independence is handled with copula models, where the event probabilities are translated to the probability of some quadrant of multidimensional space. Typically this quadrant is evaluated under gaussian or student-t distributions, where correlation is easy to define and compute.
There has been much debate in recent years about whether these models are truly capable of dealing with small quadrants, which correspond to tail events.
For more information, please see this paper by Hull et alia