A contrived example... given
FOO=\"/foo/bar/baz\"
this works (in bash)
BAR=$(basename $FOO) # result is BAR=\"baz\"
BAZ=${BAR
Modified forms of parameter substitution such as ${parameter#word} can only modify a parameter, not an arbitrary word.
In this case, you might pipe the output of basename to a dd command, like
BAR=$(basename -- "$FOO" | dd bs=1 count=1 2>/dev/null)
(If you want a higher count, increase count and not bs, otherwise you may get fewer bytes than requested.)
In the general case, there is no way to do things like this in one assignment.