One of my theories is that the Inspector is like Moses and the Birling family is like the Pharaoh. The Pharaoh in the Bible decides to free the slaves, but then doesn't go through with it so God punishes him. In the book Mr. and Mrs. Birling originally doesn't accept any blame for what they did to "Eva Smith" but then the Inspector changes their minds. But soon after the inspector was exposed as being "not a real inspector" they revert to their old mindset (except Eric and Sheila), just like the Pharaoh does.
I believe in the introduction of the play it briefly mentions the seven deadly sins. Below is who I believe represents each sin.
7 deadly sins and possible character representations:
Gluttony (Mr. Birling/Gerald/Mrs. Birling)
Greed (Birling/Gerald/Mrs. Birling)
Sloth (Eric? I don't fully understand the definition of sloth)
Pride (Gerald/Mr. Birling/Mrs. Birling)