As someone who has run many half marathons, one marathon and followed several training programs: no, that is not what happens. If you have not finished your training the only thing which happens is that you will probably run slower than you would have if you had finished your training. A common advice is to not follow the plan slavishly because that way there is only injury and burnout.

So, yes, races are deadlines but not deadlines you can rush towards because then your body will break and then you will fail the race for real. You still need to slowly and consistently build up your body just like if there was no deadline at all. It is much better to not have finished your training than to be injured.

> You can, however, create a system in which you consistently increase the number of miles you run.

This is indeed how you become a fast runner and how most training plans work, except they often peak at a mileage most people do not want to sustain to top the form right before the race.