  The tachyon effective field theory describing the dynamics of a non-BPS
D-$p$-brane has electric flux tube solutions where the electric field is at its
critical value and the tachyon is at its vacuum. It has been suggested that
these solutions have the interpretation of fundamental strings. We show that in
order that an electric flux tube can `end' on a kink solution representing a
BPS D-$(p-1)$-brane, the electric flux must be embedded in a tubular region
inside which the tachyon is finite rather than at its vacuum where it is
infinite. Energetic consideration then forces the transverse `area' of this
tube to vanish. We suggest a possible interpretation of the original electric
flux tube solutions around the tachyon vacuum as well as of tachyon matter as
system of closed strings at density far above the Hagedorn density.
