We have analyzed archival EXOSAT observations of 4U 0614+091 as recorded by the Medium Energy experiment (2-10 keV). The data set consists of five spectra, all associated with low X-ray luminosities (L(X,1-20 keV) less than or equal to 2 x 10(36) ergs s(-1), d = 2 kpc). The spectrum corresponding to the highest intensity state (F-X = 3.9 x 10 ergs cm(-2) s(-1)) is well fitted by the combination of a steep power law with a photon index of 2.7 and a relatively strong 1.5 keV blackbody component carrying off 25% of the total 1-20 keV luminosity. The two spectra associated with the lowest X-ray fluxes (F-X = 1.2, 1.1 x 10(-9) ergs cm(-2) s(-1)) are adequately described by the sum of a harder power law (photon index similar to 1.9) and a cooler blackbody component (similar to 0.5 keV) carrying of 6% and 10% of the 1-20 keV flux, respectively. Finally, for the two other spectra with slightly larger X-ray fluxes (F-X = 1.5 x 10(-9) ergs cm(-2) s(-1)), both are best fitted by a single power law (photon index similar to 2.1-2.2), and an upper limit of similar to 10% on the contribution of any blackbody component with temperature between 0.5 and 1.5 keV has been derived. 4U 0614+091 enlarges the list of X-ray bursters displaying a hard power-law spectrum in X-rays at low-luminosity states, as well as a clear anticorrelation between spectral hardness and intensity. The EXOSAT results show that when the contribution of the blackbody component reaches 25% of the total 1-20 keV flux, the spectrum steepens. This result strengthens the idea that the presence of a strong blackbody emission (most likely originating from the surface of the compact object) may be responsible for the quenching of the high-energy emission in high-luminosity neutron star systems. On the other hand, the same data show also that when the blackbody component contributes, less than similar to 10%, it does not affect the high-energy emission of the system. The EXOSAT results may also account for the fact that 4U 0614+091 was previously detected by HEAO 1 A-4 up to 80 keV, when the source was probably in a very low state. Both the HEAO 1 A-4 and EXOSAT results add support to the hypothesis that X-ray bursters emit low-flux, hard X-ray tails when they reach low-intensity states.