Last night I just encountered an uncommon situation. We were playing MD and in the rally, our team hit the shuttle, it stuck in the white tape of the net (not in the net) and didn't drop down to the floor , with the shuttle cork base leaned towards our side. 4 of us were both confused which side should be given to the point to, so we decided to give point to our opponent, as we assumed that we had finished hitting but the shuttle didn't touch the floor or any of the opponent's body during its flight. I remember there's a clip on Youtube for this circumstance, but cannot find it for reference at this moment. I'm so grateful if anyone can help me to clarify this confusion.
@Marlboro is correct; this is a let: Only if the shuttle is caught on your side, it would be a fault per §13.3.2.
Note that it is only a "let" after service has been returned but it is a "fault" during the service (to the serving side):
Apparently, sticking the shuttle on the net requires a special skill. Without going much into the aerodynamics of the asymmetric projectiles and stuff, have a look at this clip from Mens singles final from the recently concluded Dutch Open - http://bit.ly/2MDXIWZ The umpire can be heard to say 'Let' albeit softly and belatedly and at least couple three times; nonetheless, a correct decision in terms of applying the current laws.