all updates fail when one package is broken

[Humphrey van Polanen Petel]

update-manager reports "failed to download repository information"
then offers to install some updates
but then reports "the package system is broken"
and when clicking <OK> just terminates.

update-manager should install what it can rather than install nothing.

This is especially bad when it thereby prevents install of important security updates.

ProblemType: Bug
DistroRelease: Ubuntu 16.04
Package: update-manager 1:16.04.4
ProcVersionSignature: Ubuntu 4.4.0-45.66-generic 4.4.21
Uname: Linux 4.4.0-45-generic x86_64
ApportVersion: 2.20.1-0ubuntu2.1
Architecture: amd64
CurrentDesktop: Unity
Date: Thu Nov 3 10:30:18 2016
DpkgHistoryLog.txt:

DpkgTerminalLog.txt:

GsettingsChanges:
 b'com.ubuntu.update-manager' b'show-details' b'true'
 b'com.ubuntu.update-manager' b'window-height' b'422'
 b'com.ubuntu.update-manager' b'first-run' b'false'
 b'com.ubuntu.update-manager' b'window-width' b'484'
 b'com.ubuntu.update-manager' b'launch-time' b'1478127535'
InstallationDate: Installed on 2015-09-08 (421 days ago)
InstallationMedia: Ubuntu 14.04.2 LTS "Trusty Tahr" - Release amd64 (20150218.1)
PackageArchitecture: all
SourcePackage: update-manager
UpgradeStatus: Upgraded to xenial on 2016-08-05 (89 days ago)

[Humphrey van Polanen Petel (hpvpp)]

update-manager didn't crash after running "sudo apt-get install -f", but the updates still don't get applied.