I am in Xubuntu 16 today. xfce4-screensaver is in later versions but missing here:

I found it, but the install process looks technical. Not compiling yet I use .deb, standalone, etc.

There is a Power Manager I have seen blanking the screen, but it is not working here.

Is there an easy way to install a Xubuntu screensaver?

Ubuntu v. 16, both the regular version and the LTS, reached end of life some time ago.

you cannot install anything on ubuntu 16, the official repos are already removed. It is not the package itself. If you still want to put anything onto that host you need to solve it by yourself. There is no official way.
https://ubuntuforums.org/showthread.php?t=2475504
or you might try to use something from here: https://old-releases.ubuntu.com/releases/16.04.6/
or from here: https://fr.archive.ubuntu.com/

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Thanks for clarifying the evil I've noticed yet not been taught. Old Ubuntu repositories are accessible in non-Ubuntu Ubuntu-based distros. I've found them not identical but useful.

Ubuntu is basically trying eliminate their old versions, just like Microsoft. The gist is commercial if new hardware is demanded for obligatory OS updates.

I would be happy with any basic Xubuntu screensaver, but I have made progress:

The builtin Power Manager offers three display modes:

1. blank
2. sleep
3. turn off

Blank is not working in Xubuntu 16, but it will sleep.

For the time being, power management sleep is my screensaver.

There is a MATE screensaver that looks just like the XFCE screensaver present in the same EOL Ubuntu variant (rebranding?).