I beleieve the answer is no. Let's think about this for a second. Based on
what you described, I think you scenario is as follows:
You have a task that takes 2 weeks to complete (Fixed Duration). The task
will end in two weeks, but a week goes by and the task didn't get started so
you want to reschedule the uncompleted work, which will push out the start
date to a future date, but the work is still two weeks (fixed duration). How
can you expect that the finish date will not change?
The only way I can see how this can be done is if the task was fixed work
and you increase the allocation, meaning you add more resources to the task,
but that assumes the task is such that adding more resources can get the task
done sooner. But you indicated this is a fixed duration task, so that still
will not work.
