Error is caused by the upgrade of java runtime enviroment to version 11. On my system, after upgrade I had both openjdk-8-jre and openjdk-11-jre. The version 11 is favored by the /etc/alternatives settings, and jabref fails.
If you remove the jdk-11 packages and keep only the version 8, then the jabref starts as usual.
Why is this happening now? The jabref starter script provided by Ubuntu packaging (/usr/bin/jabref) has this
if ! ( echo "$JAVA_VERSION" | grep -q '1.8.0' ) ; then
# We need some options to start this version on openjdk9 and later
# See http://discourse.jabref.org/t/cannot-start-jabref-3-7-3-6-using-java-9-on-ubuntu-16-04/361/8
However, the se-ee modules were deprecated in JDK 9 so they are not present in JDK 11.
I'm still checking on how the jabref (as packaged for Ubuntu) can be fixed.
The short term fix is to run it with Java 8.
On our RedHat linux systems, we have run into the problem and the tech assistant here says that if you get the full Java packages from Oracle, they still have the needed components, but I don't know where the truth lies. I'll keep checking.