I learned a few things while trying to do this fix.
For instance, there are many ways that zippers fail. It's not always necessary to replace the whole thing. Sometimes a new zipper slider or bottom stop is enough to fix a coat opening from the bottom.
It's possible to buy parts separately or to get a kit.
I had to replace the whole thing because the teeth were too badly worn.
Hardest bit was getting the old stitches out to get the zipper off (was very well put together).
@rek
How do you replace a #zipper slider? (top part for pulling it with the fingers broke)
Do you happen to have a link?