A search for compressed supersymmetry in the stau-neutralino () coannihilation region is presented. The search targets final states with exactly one low-energy (``soft'') hadronically-decaying lepton and large missing transverse momentum () due to the natural kinematic boost from a high transverse momentum jet from initial state radiation (ISR). The data sample corresponds to an integrated luminosity of 77.2 fb of proton-proton collisions at TeV collected with CMS detector at the CERN LHC in 2016 and 2017. The distribution of the transverse mass between the and the is found to be consistent with the standard model predictions. Upper limits are set on the cross section for chargino () and neutralino () production with an associated ISR jet. For a compressed mass spectrum scenario in which the mass difference between the and the is 50 GeV, an upper limit of 290 GeV is set on the mass of the , which exceeds the sensitivity obtained by other searches to date. Finally, the results are also interpreted considering direct production of pairs with associated ISR jets.