The articles online about the linden tree emphasize
that the name for Linden's inner bark,
"bast",
ultimately resulted in that "basswood" name, oddly enough --
not the wood for carving, but rather the inner bark of the same tree.

Said linden 'bast' was in fact used in ancient cultures,
and in some archaic cultures that survived into more contemporary times,
for the raw material for fabric and garments.

If I read right, this turns up in, of all places, Japan.