Well, I am happy to deal more with An Inspector Calls because the original answerer dealt mostly with All My Sons and Death of a Salesman.

The end of An Inspector Calls deals with the family first trying to cover themselves in light of the actual situation (of implied guilt for the murder of Eva Smith) and then wondering who Inspector Goole actually is.  The suspense of the end is supposed to shock the audience.  There is a phone call and an inspector is on the way over to investigate the murder of a young woman.  (The audience realizes this is what is being dealt with during the whole play!)

Now let's put this suicide of Eva Smith in the context of the other two discussed above.  Eva Smith drank disinfectant, ... and EVERY member of the family has something to do with the death: one fired her, one threatened to get her fired from EVERY job, one had an affair with her, one denied her help in her poverty, etc.

I suppose the grand connection is as follows:  whose fault is it?  The actual answer is that we are ALL our brother's keeper!  Each person in each work of literature has some culpability in regards to the deaths of these poor, suicidal, people. 

I haven't read An Inspector Calls, but I am pretty familiar with All My Sons and Death of a Salesman.  At the end of both, the protagonists Joe Keller and Willy Loman commit suicide because their notions of the American Dream have failed them.  In All My Sons, it is unclear exactly why Joe kills himself and some may assume that it is because he does not want to turn himself in to the authorities and answer for his crime.  However, the overall context of the play suggests that Joe committed the crime to continue to be financially secure and pass the business to his sons--Joe's notion of the American Dream.  Now that everyone knows that he is guilty, his surviving son Chris does not care about the business and is angry with Joe for his actions.  I think Joe commits suicide because he feels that he has failed his family.  Similarly, Willy in Death of a Salesman believes that being a successful business man is important to his family and when he cannot live up to that image, he also feels like a failure.  So in these ways, the two plays are similar.