Using extremely deep PACS 100- and 160   μm Herschel data from the GOODS-Herschel program, we identify 21 infrared bright galaxies previously missed in the deepest 24   μm surveys performed by Spitzer/MIPS. These MIPS dropouts are predominantly found in two redshift bins, centred at z ~ 0.4 and  ~1.3. Their S100/S24 flux density ratios are similar to those of local (ultra-) luminous infrared galaxies (LIRGs and ULIRGs), whose silicate absorption features at 18   μm (at z ~ 0.4) and 9.7   μm (at z ~ 1.3) are shifted into the 24   μm MIPS band at these redshifts. The high-z sub-sample consists of 11 infrared luminous sources, accounting for  ~2% of the whole GOODS-Herschel sample and putting strong upper limits on the fraction of LIRGs/ULIRGs at 1.0 < z < 1.7 that are missed by the 24   μm surveys. We find that a S100/S24  >  43 colour cut selects galaxies with a redshift distribution similar to that of the MIPS dropouts and when combined with a second colour cut, S16/S8  >  4, isolates sources at 1.0 < z < 1.7. We show that these sources have elevated specific star formation rates (sSFR) compared to main sequence galaxies at these redshifts and are likely to be compact starbursts with moderate/strong 9.7   μm silicate absorption features in their mid-IR spectra. Herschel data reveal that their infrared luminosities extrapolated from the 24   μm flux density are underestimated, on average, by a factor of  ~3. These silicate break galaxies account for 16% (8%) of the ULIRG (LIRG) population in the GOODS fields, indicating a lower limit in their space density of 2.0 × 10-5 Mpc-3. Finally, we provide estimates of the fraction of z < 2 MIPS dropout sources as a function of the 24-, 100-, 160-, 250- and 350   μm sensitivity limits, and conclude that previous predictions of a population of silicate break galaxies missed by the major 24   μm extragalactic surveys have beenoverestimated.