This question is a bit confusing and I am sorry I do not have any code to provide. I am just interested in knowing if this is generally possible or if it is a limitation of chrome extensions.

Currently, I am thinking of building a chrome extension which should have a "Manual Select button". When this button is clicked, users should be able to highlight (or select) text on the Chrome DOM using their cursor. The text they highlight or select should then be saved and displayed in the Chrome extension (I am guessing I will put that in local storage or something). The problem I am facing with this idea, is that I notice Chrome extensions close when you click away meaning the text you select will not be saved in the Chrome extension. Is there any way to force the extension to stay open even if you click away? Or, is there a way to have the extension still run the button's function logic while it is closed?

If this is possible and can provide some sudo code of how this would work it is greatly appreciated!