I learnt from Microsoft website that they are ending support for Silverlight by Oct 2021. I am trying to understand how it will effect end users. We are user of an application which has it's user interface in Silverlight. So what Microsoft is going to do with Internet Explorer? I mean will Silverlight always be there in the browser (IE11)? On their website they mentioned it will be stopped for IE10 by Jan 31, 2020. What about IE11?
You may find more information in Microsoft's article Silverlight End of Support.
The most pertinent information for your answer is:
What happens on October 12, 2021? Will existing applications stop working?
Microsoft is not planning to take any specific action to terminate Silverlight applications. After this date, however, Silverlight will be in an unsupported state and will not receive any future quality or security updates.
This means that Silverlight will be unsupported, but will continue to work. After October 12, 2021, Silverlight will stay frozen as-is (I assume except for very serious security bugs).