There is evidence to suggest that the Inspector wasn’t a person at all. First of all the name ‘Goole’ represents a ghost (ghoul) and also the ending of the play is quite strange. It ends by a phone call from the police about a girl who has just committed suicide (repeating the whole story again). On the other hand, there is also evidence to suggest who could be real as he actually rung the doorbell to be invited into the house. If he was in fact a ghoul he would most probably have just appeared.
Another theory is that Goole is a worker from Birlings Company that may have got fired in the same strike as Eva Smith did, maybe he is just trying to gain revenge from Birling since he had ruined Goole’s career. Inspector Goole is very rude towards the Birling family and shows his dislike of them very clearly. He might have found unimportant pieces of information about each family member and inflated each problem so that it fitted in with the suicide of the young lady (Goole could have actually murdered her and is creating a story with what the Birlings have admitted). This is his way of taking revenge. He could be a man with a grudge against the family.
To begin with, I thought Inspector Goole was a jealous journalist trying to destroy the reputation of the family. The journalist gets them to admit their wrong-doings and sells it to the press. This makes the neighbourhood percept the Birlings as a bad family.
Inspector Goole is a very conniving, manipulative man. He’s very good at fooling the Birling’s into confessing. He also seems a bit religious when he includes in his final speech “taught in blood and fire and anguish”. This quote may represent Hell.
Also, using the final speech again as evidence, Goole could just be a neutral person trying to show the Birling family what they’re doing wrong. He is just trying to show people who think they’re great that they’re not really all that good.
I think the most likely theory of the choices above would be that Inspector Goole is in fact a ghoul, like a Scrooge type character.