During the process of making elastomeric laminates, elastic material is advanced and stretched in a machine direction and may be joined with one or more substrates advancing in the machine direction. During the assembly process, one-way snare apparatuses and methods may be configured to automatically isolate elastic materials that may break. The one-way snares may include a housing and a snare member movably connected with the housing, wherein the snare member is movable relative to the housing between a first position and a second position. The one-way snares are adapted to permit advancement of continuous elastic strands in a first direction through the housing when the snare members are in the first position, and to prevent an end portion a broken elastic strand from retracting in a second direction through the housing when the snare member is in the second position, wherein the second direction is opposite the first direction.