I've borked this one good.
To start I deleted some files that were apparently needed by the printer driver (Brother dcp9055cdn). I get

Reading package lists... Done
Building dependency tree
Reading state information... Done
Note, selecting 'dcp9055cdnlpr:i386' instead of '/home/shakespeare/dcp9055cdnlpr-1.1.1-5.i386.deb'
dcp9055cdnlpr:i386 is already the newest version (1.1.1-5).
0 upgraded, 0 newly installed, 0 to remove and 12 not upgraded.

I'm using a 64-bit Xubuntu, and the 386 packages were updated recently. If anybody can help, I will be eternally in their debt.

Have you tried to download & reinstall printer drivers?
https://support.brother.com/g/b/down...n_eu_as&os=128

What command are you running in your first post, you only posted the error.

Have you tried "apt -f install" to fix broken install files.

I tried:
sudo apt -f install
I need the directories for installation.

Ok. with apt, uninstall, purge autoremove, and any other apt commands that get rid of every last trace.

Then start over, read in advance and investigate any errors the small print.

May have to force the uninstall then re-install:

You are a genius, for suggesting this
sudo dpkg -r --force-all dcp9055cdnlpr
sudo dpkg -i --force-all /home/shakespeare/dcp9055cdnlpr-1.1.1-5.i386.deb

shakespeare@RYZEN:~$ sudo dpkg -i --force-all dcp9055cdnlpr-1.1.1-5.i386.deb
Selecting previously unselected package dcp9055cdnlpr-1.1.1-5.i386.deb
(Reading database ... 768649 files and directories currently installed.)
Preparing to unpack dcp9055cdnlpr-1.1.1-5.i386.deb ...
Unpacking dcp9055cdnlpr:i386 (1.1.1-5) ...
Setting up dcp9055cdnlpr:i386 (1.1.1-5) ...
shakespeare@RYZEN:~$ sudo dpkg -i --force-all dcp9055cdncupswrapper-1.1.1-5.i386.deb
(Reading database ... 768677 files and directories currently installed.)
Preparing to unpack dcp9055cdncupswrapper-1.1.1-5.i386.deb ...
lpadmin: The printer or class does not exist.
[ ok ] Restarting cups (via systemctl): cups.service.
Unpacking dcp9055cdncupswrapper:i386 (1.1.1-5) over (1.1.1-5) ...
Setting up dcp9055cdncupswrapper:i386 (1.1.1-5) ...

Is there something which would make the thing fail?

Why do you think it failed? I don't see any critical errors.
Although you did install the file twice and did not remove it first, but it looks like it worked.

Can you add the printer in your printer settings or from http://locahost:631?

The message from Xubuntu is:

[Settings]
Description: DCP9055CDN
Location: In the office.
Device URI: dnssd://Brother%20DCP-9055CDN._pdl-datastream._tcp.local/
Make and Model: Brother DCP-9055CDN CUPS
Printer State: Processing - Unable to locate printer.

The "Printer State" is the serious one.
Which "Device URI" do you have?

Did you delete the printer from CUPS and re-add it?
I don't have that printer, so not sure what protocol it is expecting, so you might have to try a few.

I have deleted it many times. The message is:
[Settings]
Description: DCP9055CDN
Location: In the office.
Device URI: dnssd://Brother%20DCP-9055CDN._pdl-datastream._tcp.local/
Make and Model: Brother DCP-9055CDN CUPS
Printer State: Processing - Unable to locate printer.

Is there something in the Device URI?

cups should have a couple of logs in /var/log/cups (error and access). is there anything either of those that might provide more detail?

The device URI is currently using the CUPS DNS-SD backend, which relies on mDNS to be working. Is Avahi hostname resolution working?

Something like...
Check the hostname resolution configuration....

1 members found this post helpful.

shakespeare@RYZEN:/$ cat /etc/nsswitch.conf
# /etc/nsswitch.conf
#
# Example configuration of GNU Name Service Switch functionality.
# If you have the `glibc-doc-reference' and `info' packages installed, try:
# `info libc "Name Service Switch"' for information about this file.

passwd: compat systemd
group: compat systemd
shadow: compat
gshadow: files

hosts: files mdns4_minimal [NOTFOUND=return] dns myhostname
networks: files

protocols: db files
services: db files
ethers: db files
rpc: db files

netgroup: nis
shakespeare@RYZEN:/$

There is an [unknown] error in the IP addresses.
99 becomes 109. Is this related to the CUPS-SD which relies on mDNS to work.
shakespeare@RYZEN:~$ ping 192.168.2.99
PING 192.168.2.99 (192.168.2.99) 56(84) bytes of data.
From 192.168.2.109 icmp_seq=1 Destination Host Unreachable
From 192.168.2.109 icmp_seq=2 Destination Host Unreachable
From 192.168.2.109 icmp_seq=3 Destination Host Unreachable
From 192.168.2.109 icmp_seq=4 Destination Host Unreachable
^C
--- 192.168.2.99 ping statistics ---
4 packets transmitted, 0 received, +4 errors, 100% packet loss, time 4525ms
pipe 4
shakespeare@RYZEN:~$