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If the separation between two atoms is shorter than the resonant wavelength, the light-mediated resonant dipole-dipole interaction (RDDI) will be significant. RDDI is usually long-range, dissipative, and lead to phenomena such as super and sub-radiance. For different light fields, such as the 3D free space or field engineered by photonic devices, RDDI could have completely different forms. However, in 1D atom arrays with a few atomic excitations, we show that some properties are universal (under some loose conditions) regardless of the underlying light fields. This includes a power-law scaling of the decay rate of the subradiant states, and multiply-excited states interpreted as Jordan-Wigner fermions or Tonks-Girardeau bosons.