This method of connection (shield to the insensitive end) has been used in pro audio since Cain first cryo’d Able’s tubesIf by "insensitive end" you mean the amplifier end - as George stated - then you are completely confused.
First, we’re talking here about single-ended connections. Pro-audio uses balanced connections.
Second, the purpose of the extra shield is to minimize noise. One way to do that is to have all grounds at the same potential. To best achieve that, you need to tie all the shields together at one common point. What common point do all components in a system share? The source, of course.
I have never seen a manufacturer of SE cables that uses the extra outer shield designate cable direction in any way other than the shield being connected at the source end.