  We show that for a tangle $T$ with $-\partial^0T \cong \partial^1 T$ the
Hochschild homology of the tangle Floer homology $\widetilde{\mathit{CT}}(T)$
is equivalent to the link Floer homology of the closure $T' = T/(-\partial^0T
\sim \partial^1 T)$ of the tangle, linked with the tangle axis. In addition, we
show that the action of the braid group on tangle Floer homology is faithful.
