Halina Lewandowski and Yasser Ayad Are you both running with Patch 2 (Pro 2.3.2)?
Can you provide more details about what types of features continue to show up in the export that are outside of the clipped boundary (Points, lines, polygons, text...?) and how those are symbolized?
Any screenshots of how the map clipping itself is set up?
What you describe would be a bug, yet I don't see anything in the system describing this. When I test on a daily build of 2.4, here is what I see:
Map with no clipping:
Clipped to Riverside county:
Exported to PDF and viewed in Adobe Acrobat Reader DC:
Here is how the clipping is set up:
'Clip to the outline of features' using the Selected option.
Please provide more details so that we can understand the issue you're seeing. It might also be a good option to call Technical Support to report something that you feel is a bug:
https://support.esri.com/en/contact-tech-support