Reported in SOLR-14515 (private) and fixed in SOLR-14561 (public), released in Solr version 8.6.0. The Replication handler (https://lucene.apache.org/solr/guide/8_6/index-replication.html#http-api-commands-for-the-replicationhandler) allows commands backup, restore and deleteBackup. Each of these take a location parameter, which was not validated, i.e you could read/write to any location the solr user can access.
Apache Solr 5.0.0 to Apache Solr 8.3.1 are vulnerable to a Remote Code Execution through the VelocityResponseWriter. A Velocity template can be provided through Velocity templates in a configset `velocity/` directory or as a parameter. A user defined configset could contain renderable, potentially malicious, templates. Parameter provided templates are disabled by default, but can be enabled by setting `params.resource.loader.enabled` by defining a response writer with that setting set to `true`. Defining a response writer requires configuration API access. Solr 8.4 removed the params resource loader entirely, and only enables the configset-provided template rendering when the configset is `trusted` (has been uploaded by an authenticated user).
The 8.1.1 and 8.2.0 releases of Apache Solr contain an insecure setting for the ENABLE_REMOTE_JMX_OPTS configuration option in the default solr.in.sh configuration file shipping with Solr. If you use the default solr.in.sh file from the affected releases, then JMX monitoring will be enabled and exposed on RMI_PORT (default=18983), without any authentication. If this port is opened for inbound traffic in your firewall, then anyone with network access to your Solr nodes will be able to access JMX, which may in turn allow them to upload malicious code for execution on the Solr server.