Liquid metal (LM) has recently been used as an advanced stretchable material for constructing stretchable and wearable electronics. However, due to the poor wettability of LM and the large dimensional change during stretching, it remains very challenging to obtain a high conductivity with minimum resistance increase over large tensile strains. To address the challenge, an LM-superlyophilic and stretchable fibrous thin-film scaffold is reported, on which LM can be readily coated or printed to form permeable superelastic conductors. In contrast to conventional LM-based conductors where LM particles are filled into an elastic matrix or printed on the surface of an elastic thin film, the LM can quickly infuse into the LM-superlyophilic scaffold and form bi-continuous phases. The LM-superlyophilic scaffold shows unprecedented advantages of an extremely high uptake of the LM and a conductivity-enhancement characteristic when stretched. As a result, the LM-based conductor displays and ultrahigh conductivity of 155 900 S cm−1 and a marginal resistance change by only 2.5 fold at 2 500% strain. The conductor also possesses a remarkable durability over a period of 220 000 cycles of stretching tests. The printing of LM onto the LM-superlyophilic scaffold for the fabrication of various permeable and wearable electronic devices is demonstrated.