What Happens to the Teeth Underneath Veneers over Time?

Tooth structure beneath veneers usually have nothing significant happen to them over time. If maintained properly, nothing happens that would not ordinarily happen. 
Over time, teeth naturally darken or yellow. If the veneers are extremely thin, this discoloration MAY show through, but not necessarily.

If the veneers are placed properly and proper bonding protocols are used you should not have an issues.

The teeth will not rot if you take care of them. 

The veneers will not make your breath stink if you brush and floss properly. The porcelain is very smooth and does not trap food.

As long as veneers were properly bonded and and are well maintained (brushing and flossing), the teeth underneath are isolated from the oral environment. This means nothing will happen to them. When they are sealed off in this way, there is no odor and no decay.

As your already know veneers are a thin porcelain facing that is bonded to the front surfaces of your teeth. Before the veneers are bonded, the teeth that will receive the veneers are disinfected and a composite cement is used to seal the teeth under the veneers. This seal is very strong and should not allow for contamination of the teeth under the veneers.
Thus because the teeth are sealed under the veneers there should be no risk for odors which is a may be a result of bacteria.
When veneers are properly placed and regularly maintained like natural teeth, they can last a long time a provide you with many years of beauty.

Excellent question. As long as an experienced cosmetic dentist did the work, and you take care of your teeth and veneers as instructed, your teeth will remain healthy over time. An experienced dentist will give you a result that looks good, feels good, and lasts a long time.