Description of problem:
I had to temporarily remove Emacs and the uninstall pulled some system core libraries.
A small note before you check the attached fpaste: the 'garbage' you see between the output of the 'dnf remove' command and the output of the 'dnf' command is a mix of dnf plugins crashing.
Now, here's the log: http://paste.fedoraproject.org/307960/52108940/
And here is the --sysinfo: 

Version-Release number of selected component (if applicable):
F23, fresh installation, up to date.
Non-official repositories includes: RPMFusion (all), Fish shell (fishshell.com) and two Copr repos, one for Lollypop (a music player) and the other for Cutegram, a Telegram client.
dnf: 1.1.5
Emacs: 24.5

How reproducible:
Didn't try again yet.

Steps to Reproduce:
1. As shown in the attached log
2.
3.

Actual results:
Dnf will become unusable. I had to manually download the sqlite RPM file, uncompress and copy its contents to the original locations.

Additional info:
One strange thing I noted when reinstalling sqlite and the the libraries is that for dnf it was like they were indeed installed as if the local database wasn't refreshed.

Best!