Uhhh ... we're not getting the entire story here!
Yes, cron execution is suspended until an upgrade to core code completes.
So, did you attempt to upgrade your Moodle code?
There is a version.php file at the root of your moodle code that shows the version and build date of the core code. What does that file show? It is one of the files that would be changed upon an upgrade so the date/time stamp of the file could also be a clue.
Did you do an environment check and update the component then use the drop down pick list of moodle versions to see if your server met requirements? PHP version + php extensions, MySQuL version, database character set/collation, etc.?
Are you on shared hosting? Did you use a 'one click wonder' to upgrade (like the infamous Softaculous)?
'SoS', Ken