Edit: ( I have revised my answer as it was originally a bit misleading)
Some opinions hold that only if the pitam fell off in the early stages of the esrog's growth, does the esrog remain kosher. In such a case:
If there is an indentation at the tip of the Chotem, where the pitam
was once attached, this is a clear indication that the pitam fell off
in the early stages of the esrog's development, and the esrog is
kosher. Another indication that the pitam fell of in the early satges
of the the esrog's growth is a thin groove that encircles the area of
the fallen pitam.
However some authorities are more lenient, and hold that a pitam that fell off even immediately before the esrog was picked does not render the esrog pasul.
In this case - then the following would be a sign that the pitam naturally fell off and would be kosher:
A clear indication that the pitam was fully dried while still on the
tree is the presence of a scab that *fully cover*s the place where the
pitam was severed...
If the place of the pitum is only partially covered with the scab ,
then it must be assumed that it was still partially attached while on
the tree , and only fell off later , after the esrog was picked;
consequently, the esrog must be considered pasul.
(Source: The four minim - apractical illusrated guide - by R. Avraham Chaim Adess [feldhaim publishers] - pp154-158)
I myself have seen a esrog with a broken pitum - and I can testify to the above. (ie - you don't see a nice clean scab but rather a bumby/jagged surface.