Examples of dynamic page content

I am at a bit of a loss how to describe this, but I will give it a go.

We have a system that displays status of shall we say ‘tasks’

There could be 100s of tasks. The user will want to filter and sort these tasks so that a subset is displayed on the screen. After filtering and sorting therefore, the screen will show the top 50 for instance.

Things happen though in real time. Tasks are completed, or become overdue and change in priority. What was the top 50 may no longer be.

Ideally the client should be asking the server if the top 50 has changed and then it could display a message to the user advising to refresh. We don’t want this to happen automatically as it will be disorienting to the user.

I’m looking for some examples of this type of behaviour so that we can have a better discussion with stakeholders.

Any suggestions gratefully received.

How does the system know that tasks are competed or have changed in priority? Does someone have to enter this info, or is it something the system would be expected to know (such as some kind of digital task)?

Tasks might be completed by others on another part of the system, or by remote pieces of equipment. This is the back-office management station.
Imagine like this forum, I could have the threads listed with the most number of responses at the top. If I just left the screen on that page with no refresh, what was shown as the most active thread a few hours earlier might now not be. plus there would be brand new threads that I would want to see.
In a way, its a bit like Twitter where a box appears that says ‘5 new tweets’ then ‘6 new tweets’ etc - except that in my scenario, the order of the tweets could also change.