Years ago I learnt a hard lesson about ligatures. They don't alway print as you see on your screen... funny characters can appear.
What I I do is... always turn off ligatures... as a matter of fact, I unselect it as a preference so I don't ever have to worry about it.
How about trying this... convert your PDF to postscript and run it through distiller again.
In the last ten years the only time I can recall seeing ligatures substitute or drop out in print is when the font is not properly embedded in a PDF or downloaded to the RIP when printing direct from the application. Used to be more of a problem when working cross-platform with non-unicode fonts, though.
I'm surprised that the ligature in final would be a problem, but not in finally, so I don't think it's a ligature issue, per se, but I don't know what the problem really is. Seems sort of like how type is sometimes broken up when you open a PDF in Illustrator...
These problems are difficult, and details matter a lot.
EXACTLY how are you generating the PDF, and exactly what tools are you using to view and search it?
What versions of the tools, and what version numbers of the operating systems?
Can you share the files with us?
Lilia, I don't think it's fair to spread Fear, Uncertainty, and Doubt (FUD) about ligatures. They're an important typographical element that works well for many people. If there's a problem with it, we should figure it out and get it fixed rather than ignoring it and pushing it on to the next generation.