How NBA Teams Leave Players Open To Help Their Defense

The video below shows how NBA teams in the playoffs play off of non-shooters to help on the other teams' better players.

Trapping Screens
:47 - It first shows how players aggressively help on cutters when their man sets a screen.  They often double team off of ball-screens, down screens and any situation where their man is involved in the screen.  Their defender also plays off and helps bump cutters, allowing the other defenders to help, hedge, and trap ball-handlers using screens.

Put Your Big On Non-Shooting Wings
NBA Teams also switch up their match-ups by putting a rim protecting or great help-side big on a non-shooting perimeter player.  This allows other players to pressure the ball and help with pressure, i.e. traps and hard hedges, while knowing that they have support at the basket.  This can also create mismatches on the other end, as the other team might have trouble finding their man in transition, ending up in cross match-ups.

How To Counter
One of the best ways that offenses counter the defense playing off of a non-shooter is by a well-timed cut.  When you cut and relocate against a helping defender, you can get easy lay-ups, as seen in the video.  This also puts you in great rebounding position.  

One other observation seen in the video is how effective putting your non-shooter in the short corner can be (5:45).  It goes against modern basketball wisdom to hurt your spacing, but as stated in the video, if your defender is already sagging off in help, your spacing doesn't matter as much.  The narrator calls it the 'dunk-it' spot, and it puts you in position to get a dump down layup or in position for easy put-backs (6:00).  

At the NBA level, it is well-documented that the 3 point shooters' shooting percentage goes significantly up when they are in the corner, so a good counter is to put your shooter in the corner and work in practice to help them become a better corner 3 point shooter (7:00).

7:40 - When they have a big guarding a perimeter player, get the ball to your best player and screen with the man being guarded by the post.  Doing it up high puts a lot on the big trying to stop your guard.