TL;DR Were an upgrade of OpenJDK to become necessary, versions of Cassandra >= 3.6 would not start (currently pertains to RESTBase production clusters only).
As reported in CASSANDRA-14173: Cassandra utilizes classes marked private/internal in the JDK that have been removed in OpenJDK 1.8.0_162. This has been fixed and will be released as part of 3.11.2 (RSN).
See also: T178905: Upgrade RESTBase cluster to Cassandra release: 3.11.2