Subsync is a program that will sync any subtitle file based on either audio or another subtitle. It is remarkably good at syncing any subtitle you throw at it. I never encountered anything even remotely as good as Subsync for that task.

Unfortunately, the author archived it due to some technical reasons as well as bad interactions with users. I don't believe there is anything as good out there when it comes to syncing broken subtitles. Subsync still works, but I don't know for how long. I am not a programmer. I am posting this as a call for help: if anyone is interested in maintaining this program, I think it would be of great help to a lot of people.

Right now, Subsync is a manual tool with a graphical interface. But I foresee it working in the background with programs like VLC, Plex, or Stremio. That would be awesome.

EDIT

Subsync is automated and language aware. It will sync individual lines using audio or another subtitle as a reference. It won't just shift everything; it will adjust them individually. It is usually not necessary to go through the entire file, but you can do it for badly synced subtitles. Adjusting every single subtitle will take more time, but you can do it.

Merely shifting all the subtitles won't work for older TV shows because of the breaks. Depending on the version (DVD, Blu-Ray, WEB, or recorded directly from TV), the ad breaks will be edited slightly differently, with different delay times before resuming the show. That is enough for the subtitles to lose sync after every act. There is also the issue of frame rate and perhaps other video features, which I believe can also unsync subtitles. I probably have more issues with subtitles than most because I mostly watch older or classic TV content.

(Adapted for clarification from my response below)