Subtitling systems contain 'widespread' security threat (on BBC news)

My question here is how secure is the Plex server and other Plex apps when it comes to being secure against compromised subtitle files? – OR – Can a subtitle file of any kind and any type which is infected compromise the Plex server, Plex player or both?

The short answer: Plex is not affected by this.

Here is the statement from Plex:

Plex does not share any code with any of the app vulnerabilities that were mentioned. We have reviewed equivalent areas in our own products and we are confident that Plex is not affected by any of the vulnerabilities that Checkpoint discussed.

Source: https://forums.plex.tv/discussion/272965/plex-is-not-affected-by-subtitle-vulnerabilities-noted-by-checkpoint

Try searching next time. Lots of posts on the subject.
And maybe next time make it a question, not a statement when you are not sure.