  It is shown that topologically stable cosmic strings can, in fact, appear to
end or to break, even in theories without monopoles. This can occur whenever
the spatial topology of the universe is nontrivial. For the case of
Abelian-Higgs strings, we describe the gauge and scalar field configurations
necessary for a string to end on a black hole. We give a lower bound for the
rate at which a cosmic string will break via black hole pair production, using
an instanton calculation based on the Euclidean C-metric.
