I say, with Allah's guidance: Whoever wears a slipper that cannot withstand walking a league or more — approximately five kilometers — and it tears with walking, it is not permissible for him to wipe over it. This is because one of the conditions for the permissibility of wiping over the slippers is the ability to continue normal walking in them for a league or more. Here, the condition is not met, so it is not permissible. See: Radd al-Muhtar 1: 174, Al-Maraqi p.130, Al-Durr Al-Mukhtar 1: 176, Nihayat al-Murad p.378-379, and Allah knows best.