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The production of soft photons in small systems was extensively studied in fixed-target experiments at beam momenta ranging from 10.5 to 450 GeV/c. Most experiments reported an excess of soft photons compared with the expectation from hadron decays that could not be explained by initial- and final-state bremsstrahlung. The emergence of a photon excess in a transverse momentum (pT) range far below 0.2 GeV/c was dubbed the soft-photon puzzle. At the Intersecting Storage Rings (ISR) at CERN, also an excess of dielectrons had been measured at low invariant mass and small pair pT_ee in pp collisions at sqrt(s) = 63 GeV. In ALICE the reconstruction efficiency of low-pT electrons can be increased by reducing the magnetic field of the central barrel solenoid. This allows a better electron background rejection and simultaneously enables the investigation of a kinematic domain at low dielectron invariant mass m_ee and pair transverse momentum pT_ee similar to that of the ISR experiment, which was previously inaccessible at the LHC. In this talk, a measurement of dielectron production in proton-proton (pp) collisions at sqrt(s) = 13 TeV, recorded with the ALICE detector at the CERN LHC, will be presented. The data set was taken with a reduced magnetic solenoid field of 0.2 T. The cross section for dielectron production is studied as a function of mee, pT_ee, and event multiplicity dNch/deta. Comparison of the measured dielectron yield to the hadronic decay cocktail at 0.15<m_ee <0.6 GeV/c2 and for pT <0.4 GeV/c indicates an enhancement of soft dielectrons, reminiscent of the ’anomalous’ soft-photon and -dilepton excess in hadron-hadron collisions. Acceptance-corrected excess spectra are extracted and compared with calculations of dielectron production from hadronic bremsstrahlung and thermal radiation within a hadronic many-body approach.