Care to explain that? Unless two wires are connected the link will not
function at all.

See my other post. ADSL is carried at a radio frequency (RF) so will
effectively 'jump' gaps in cables.
It does work with one wire only connected without any problems and in
some cases can work with none.
For an electrical current to flow you are quite correct though.

You are being somewhat disingenuous on this matter. In theory ADSL may work
but in practice in such a case the signal to noise ratio is likely to make
the link very unreliable with lots of drop outs. The bottom line is that an
ADSL line will only function correctly if the telephone circuit is in good
order.