This paper investigates the use of passive electrodynamic tether drag as a method for quickly removing spent or dysfunctional spacecraft from low Earth orbits (LEO). The fundamental physical principles underlying the operation of an electrodynamic drag Terminator Tether (TM) are developed, some practical considerations are discussed, and calculations of the area-time product are made for spacecraft orbits representative of those that will be used in the LEO satellite constellations of the next few decades, These calculations indicate that electrodynamic drag can remove a spacecraft from a typical 700-2000-km LEO constellation orbit within a few months using a Terminator Tether system massing less than 3% of the spacecraft dry mass, Although the tether increases the cross-sectional area of the satellite system during the deorbit phase, the electrodynamic drag is so many times greater than atmospheric drag at these altitudes that the total area-time product can be reduced by several orders of magnitude, reducing the risks of collisions with other satellites, Concerns regarding tether survivability can be solved by using a multiline, fail-safe Hoytether (TM) construction. The Terminator Tether may thus provide a cost-effective method of mitigating the growth of debris in valuable constellation orbits.