We have studied the effect of nonmagnetic Zn impurities in the coupled spin ladder Bi(Cu_{1-x}Zn_{x})_{2}PO_{6} using ;{31}P NMR, muon spin resonance (microSR), and quantum Monte Carlo simulations. Our results show that the impurities induce in their vicinity antiferromagnetic polarizations, extending over a few unit cells. At low temperature, these extended moments freeze in a process which is found universal among various other spin-gapped compounds: isolated ladders, Haldane, or spin-Peierls chains. This allows us to propose a simple common framework to explain the generic low-temperature impurity-induced freezings observed in low-dimensional spin-gapped materials.