There are two ways that I know of to make something stretch. One is to just set an ik chain on the bone you want to stretch to, and changing the bone that actually stretches to alow stretch.
2nd way is to use a stretch-to constraint. Both example are in this blend. The basic difference is one increases scale to accomadate the stretching, the other increases length but decreases in volume. What you might actually need is probably to preserve volume while increasing length. This would take some more tricky parenting than I have time to dive into right now.