We present the first observation of K^{-} and ϕ absorption within nuclear matter by means of π^{-}-induced reactions on C and W targets at an incident beam momentum of 1.7 GeV/c studied with HADES at SIS18/GSI. The double ratio (K^{-}/K^{+})_{W}/(K^{-}/K^{+})_{C} is found to be 0.319±0.009(stat)_{-0.012}^{+0.014}(syst) indicating a larger absorption of K^{-} in heavier targets as compared to lighter ones. The measured ϕ/K^{-} ratios in π^{-}+C and π^{-}+W reactions within the HADES acceptance are found to be equal to 0.55±0.04(stat)_{-0.07}^{+0.06}(syst) and to 0.63±0.06(stat)_{-0.11}^{+0.11}(syst), respectively. The similar ratios measured in the two different reactions demonstrate for the first time experimentally that the dynamics of the ϕ meson in nuclear medium is strongly coupled to the K^{-} dynamics. The large difference in the ϕ production off C and W nuclei is discussed in terms of a strong ϕN in-medium coupling. These results are relevant for the description of heavy-ion collisions and the structure of neutron stars.