synthetic chemist is the only item that gives a productivity of below -50%
thus, negative productivity is possibly if working conditions are set to below -10% (or any item combination to that effect; but there is CURRENTLY only 1 such item -- in addition to synthetic chemist -- that affects fertilizer works, for -10% productivity)
for example: productivity is -40% -- the sum of -90% (synthetic chemist) and -50% (working conditions)... except there is no below 0%
and there is of course also the old bug where change of workforce type allows setting working conditions to +50% WITHOUT affecting happiness: jornaleros -- correctly -- have affected workforce of 0; however, obreros are NOT affected either... so basically free productivity with no penalties