Package dynamsoftservice needs to be reinstalled but can't find an archive for it.

For diagnostic purposes please provide the output of the following commands (to be executed in a terminal window):

uname -a
lsb_release -crid
sudo dpkg --audit
dpkg -l | grep -i dynamsoft
apt-cache policy dynamsoftservice
ls -l /var/cache/apt/archives/*dynamsoft*.deb

Where did you get this package? Did you download it from a web site?

w5jml@w5jml-Satellite-C655:~$ uname -a
Linux w5jml-Satellite-C655 4.4.0-92-generic #115-Ubuntu SMP Thu Aug 10 09:04:33 UTC 2017 x86_64 x86_64 x86_64 GNU/Linux
w5jml@w5jml-Satellite-C655:~$ lsb_release -crid
Distributor ID: Ubuntu
Description: Ubuntu 16.04.3 LTS
Release: 16.04
Codename: xenial
w5jml@w5jml-Satellite-C655:~$ sudo dpkg --audit
[sudo] password for w5jml:
The following packages are in a mess due to serious problems during
installation. They must be reinstalled for them (and any packages
that depend on them) to function properly:
 dynamsoftservice (no description available)

The following packages are missing the list control file in the
database, they need to be reinstalled:
 dynamsoftservice (no description available)

The following packages are missing the md5sums control file in the
database, they need to be reinstalled:
 dynamsoftservice (no description available)

w5jml@w5jml-Satellite-C655:~$ dpkg -l | grep -i dynamsoft
iHR dynamsoftservice 13.0 amd64 (no description available)
w5jml@w5jml-Satellite-C655:~$ apt-cache policy dynamsoftservice
dynamsoftservice:
  Installed: 13.0
  Candidate: 13.0
  Version table:
 *** 13.0 100
        100 /var/lib/dpkg/status
w5jml@w5jml-Satellite-C655:~$ ls -l /var/cache/apt/archives/*dynamsoft*.deb
ls: cannot access '/var/cache/apt/archives/*dynamsoft*.deb': No such file or directory

I got the package from Dynamsoft as a result of trying to install WebTwain.

Then download that package again and re-install it.

Maybe you better ask at the support pages of the provider.

I tried to download and reinstall, and the installation crashes stating it cannot find an archive.

Here is the message I get when I try to reinstall the package.

This is a major failure of your software management system. Please check for broken packages with synaptic, check the file permissions and correctness of the file '/etc/apt/sources.list' and reload the software information with: 'sudo apt-get update' and 'sudo apt-get install -f'.

How is that package installed?
Is there a repository for automatic download by the package management system, or do you have to manually download it?

I manually downloaded it.

Here are the results from your instructions:

w5jml@w5jml-Satellite-C655:~$ sudo dpkg --install Downloads/DynamsoftServiceSetup.deb
(Reading database ... 290443 files and directories currently installed.)
Preparing to unpack .../DynamsoftServiceSetup.deb ...
Unpacking dynamsoftservice (13.0) over (13.0) ...
Setting up dynamsoftservice (13.0) ...
28:/opt/dynamsoft/WebTwainService/WebTwainCertCheckMgr&

How can I tell if it did any good?

For verification run the command

sudo dpkg --audit

This command shows problems in the package management system, i.e. if you get no output, then the repair action has worked.
If you get output, please copy/paste it, that we can see.

I ran the command, sudo dpkg --audit, as directed and got no output. Thank you so much for your help, everything seems to be back in order.

Thanks Manfred Hampl, that solved my question.