There is a command line method of keeping the video live on a Mac. According to notes on the VLC forum, the behavior has changed. I am using am M1 Macbook Air in Fall 2022 on Mac OS X 12.3.1 Monterey.
As I mentioned in a comment on DavidPostill's answer, unchecking 'Quit after Playback' on a Mac keeps VLC from closing, but the video still does close.
Someone at VideoLan (nickname: VLC_Help) on the forum mentioned the VideoLan wiki shows command line options to solve this however. The following of course assume your version of VLC was installed in the default location.
How to do it on a Mac:
You can add a command line 'vlc' alias for this purpose in your .bashrc or .zshrc for either shell you use with this alias:
alias vlc='/Applications/VLC.app/Contents/MacOS/VLC --play-and-pause &'
How to do it in Windows (Tested in Windows 11):
In windows, you can add the '--play-and-pause' argument in a shortcut like above to make it so you don't have to keep dropping to the command line.
If you start VLC with that command line argument, it will keep the video open after playback but stopped on the last frame.
For those of you who are unaware because you may not have used but one of them, Macs and PCs do different things whe closing applications, which is why this is a point.
Windows (usually) closes the complete app when it is finished.
Macs (and modern tablets and smartphone) usually close the current media/project within the app, but don't generally close the app itself. This makes it fast to load up later. So there is a difference between closing the video and closing the app that plays the video.
This is not unique to video player apps, but the generic regular methodology for most apps on these platforms.