Is there way to run a code every time when any cron is run?

There is such way, I guess…

When you schedule and event with wp_schedule_event all you really do is:

Schedule a hook which will be executed by the WordPress actions core
on a specific interval…

And if you’ll take a look at wp-cron.php then you’ll see, that on line 126 this happens:

do_action_ref_array( $hook, $v['args'] );

OK… So how does it solve the problem?

It does, because you can use all hook. Actions assigned to that hook are called everytime any filter/action is called.

And you can, at least I believe so, use wp_next_scheduled to check, if given hook is event hook or not.