Execute ffap-file-at-point with the following buffer contents (| for
cursor position):

7:|

The result is "", which leads to ffap's default input being ~ (not ~/ as
expected).

Similarly, try ffap-file-at-point on:

:6|

This is due to ffap-file-at-point stripping off the colon and numbers,
and sending "" to ffap-file-exists-string. (file-exists-p "") returns t,
so ffap-file-at-point treats "" as an existent file.

The following diff fixes this, but I'm not sure if it's the best
approach. Perhaps ffap-file-at-point just checks that the argument to
ffap-file-exists-string is non-empty each time it's called.