the term "chain stretch" is a bit of a misnomer. From:
"Cyclists often speak of chain "stretch", as if the side plates of an old chain were pulled out of shape by the repeated stresses of pedaling. This is not actually how chains elongate. The major cause of chain "stretch" is wearing away of the metal where the rivet rotates inside of the bushing (or the "bushing" part of the inside plate) as the chain links flex and straighten as the chain goes onto and off of the sprockets. If you take apart an old, worn out chain, you can easily see the little notches worn into the sides of the rivets by the inside edges of the bushings. With bushingless chains, the inside edge of the side plate hole that rubs against the rivet has a smooth radius instead of a sharp corner. This probably contributes to the greater durability of bushingless chains."
"You can see how the rivet of this unusually badly worn chain has been worn away.
Note also how the roller has flopped out of position."
"The reason the roller flops around is that the "bushing" part of the chain has been eroded away.
No doubt the inner surface of the roller has become enlarged as well."
They're speaking of bicycle chains, but the same thing applies to motorcycle chains. Chain "stretch" isn't actually stretch at all, but rather the wearing of the pin / rotating surfaces. When the pins are worn a sufficient amount, the accumulative "slop" or tolerance in the chain is sufficient that it "stretches" relative to the sprocket. Generally there's only a little bit of wear per pin, but there are also 108-112 links on most bikes. Multiply a small bit of wear per pin, x the number of pins in a chain, and you've got enough slop that it's noticeable.
Not to mention, once a chain starts to stretch like this, it's usually an exponential curve. Ie, it continues to wear at a -very- high rate of speed. It's not uncommon to tighten the chain on Monday, only to find it dangerously loose again by Wednesday. Not only do the links / pins eat themselves faster and faster, but the damage to the sprocket increases much quicker as well, as the chain is out of proper pitch.
Here are some pictures of some worn sprockets. As you can see, the wear of the chain, which causes the chain to lose it's proper pitch, can have devastating effects on the sprocket. This is also why, as a general rule, you should replace sprockets when replacing chains. Putting a new chain on these worn sprockets would be futile, as the old sprocket will destroy the new chain -very- quickly.
One goooOOOOood looking rear sprocket:
Good picture showing how a worn chain / sprocket can lead to the death of the other component.