If someone has an unauthorized remote connection to my computer (not remote login), can they see anything if the browser is 'not' open?

I had asked someone a while back and they stated that if someone is on your computer (most likely via malware) and the browser is closed, they have "zero" access to seeing anything you are doing (ie: terminal), or, to your files (ie: documents folder).

Just looking for a 2nd opinion since sometimes I have my internet connection active, but with no browser open, and I think I am safe from prying eyes. But am I?