Here is what I have found out so far:
PDFBox uses a resource file to bound PDF operators/instructions to certain classes which then process the information.
If we take a look at the PDFTextStripper.properties resource file under:
pdfbox\src\main\resources\org\apache\pdfbox\resources\
we can see that for instance the BT operator is bound to the
org.apache.pdfbox.util.operator.BeginText class and so on.
The PDFTextStripper under
pdfbox\src\main\java\org\apache\pdfbox\util\
takes this into account and utilizes the processing of the PDF with this classes.
BUT all graphical objects are ignored, therefore no information of underline or table structure!
Now if we take a look at the PageDrawer.properties resource file we can see that this one bounds to almost all operators available. Which is utilized by PageDrawer class under
pdfbox\src\main\java\org\apache\pdfbox\pdfviewer\
The “trick” is now to find out which graphical operators are those who represent underline and tables and to use them in combination with PDFTextStripper.
Now this would mean reading the PDF file specification, which is currently way to much work.
If someone knows which operators are responsible for which actions to draw underlines and table lines please let me know.