This is a bug with basename 5.3.0 found in the latest Cygwin 1.5.15.1.
This used to work with basename in the March 2003 version.  Sorry I
don't know the version number any more because the update removed
the old version.

$ FCF=N/A
$ echo $FCF
N/A
$ Z=${FCF:(-1)}
$ echo $Z
A
$ FCG=`basename $FCF $Z`
$ echo $FCG
A                           <====== should return 'N/'

Another simpler way to see the bug:

$ basename NA A
N
$ basename N/A A
A                           <====== should return 'N/'

Even with quoting:

$ basename 'NA' A
N
$ basename 'N/A' A
A                           <====== should return 'N/'