For my case I had to explicit remove and install again pure-ftpd via apt:

systemctl stop  pure-ftpd
apt remove      pure-ftpd
apt install     pure-ftpd
systemctl start pure-ftpd

Or if you need to use pure-ftpd-mysql instead:

systemctl stop  pure-ftpd-mysql
apt remove      pure-ftpd-mysql
apt install     pure-ftpd-mysql
systemctl start pure-ftpd-mysql

Preliminary Steps

Clean up your packages and update the cache:

sudo apt-get purge pure-ftpd
sudo apt-get autoremove
sudo apt-get autoclean
sudo apt-get update

Then try again:

sudo apt-get install pure-ftpd

If reinstalling PureFtpd doesn't work

This is line 23 of /usr/sbin/pure-ftpd-wrapper:

use File::Basename;

File::Basename is a Perl module. I tried installing it using:

$ cpan
cpan[1]> install File::Basename

But the install failed with the error:

Make had returned bad status, install seems impossible

However, it did mention that File::Basename is part of the perl-5.18.2 distribution.
So I upgraded Perl:

sudo apt-get upgrade perl --no-install-recommends

After that I could verify that it was installed using:

$ cpan
cpan[1]> i File::Basename

If you cannot install the Perl module

Question: When you use cpan and type i File::Basename, what comes up?

Response:

autouse.pm did not return a true value at /usr/share/perl/5.14/App/Cpan.pm line 182. BEGIN failed--compilation aborted at /usr/share/perl/5.14/App/Cpan.pm line 182. Compilation failed in require at /usr/bin/cpan line 8. BEGIN failed--compilation aborted at /usr/bin/cpan line 8.

Next Step:

Reinstall perl with

sudo apt-get install Perl --reinstall

OR

sudo apt-get purge Perl
sudo apt-get install Perl

(WARNING: Purging Perl can affect a LOT of dependencies and other applications)