Did you check in the Font Inspector what font(s) Firefox is using for each case?

For me Helvetica uses NimbusSanL-Regu (Nimbus Sans L) and the Arial cases use Liberation Sans, so it appears the for Arial no fallback to sans-serif is used. The last Sans-serif case uses the default font as set in Options/Preferences (DejaVu Sans) as expected. You didn't include a Serif case, so I'm not seeing the default Serif font being used. With zooming there is not much difference.

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Checked the font inspector, the five paragraphs you sent render to Bookerly, NimbusSansRegular, NimbusSansRegular, Ubuntu, Bookerly respectively.

What I don't understand is the following (for the different example lines): 1) Arial - a sans-serif font - instead of falling back to the sans-serif default (that would be Ubuntu) it falls back to the serif default (in this case Bookerly). 2) Helvetica - another sans-serif - falls back to NimbusSansRegular instead of the default sans-serif Ubuntu. I could understand this, if Arial would also resolve to NimbusSansRegular (because they both match Nimbus via fontconfig), but as you can see they are displayed differently. 3) Since Arial and Helvetica are non existent on the machine, it should revert to the third option (sans-serif). But it still uses NimbusSansRegular for some reason. I don't see the logic behind this choice. 4) and 5) are displayed as expected

The goal is that if Firefox cannot find the font (Arial, Helvetica etc) it falls back to the correct serif, sans-serif one defined by fontconfig.

I get this and that matches what I posted above.

fc-match Arial => "Liberation Sans" "Regular"
fc-match Helvetica => "Nimbus Sans L" "Regular"
fc-match sans-serif => "DejaVu Sans" "Book"
fc-match serif => "Liberation Serif" "Regular"

Do you think this is a bug, or a correct default behavior? In the latter case is there any workaround?