Is there a way to batch remove the same background from multiple images?

Someone asked me a Photoshop question the other day, and after some time thinking on it I couldn't come up with an answer - hoping someone here can shed some light!

Let's say I've got a batch of photos of people all standing in front of the same textured background - for example, headshots against a studio background. If I wanted to remove the background from all these photos, there are a few ways to go about it; the problem is all methods I know are manual, and large batches become pretty tedious.

Now, let's say the background in each photo was stationary (maybe a few px of wobble), and I had a photo of the complete background without any figure blocking it. Would there be a way to use the complete background as some sort of inverse/subtractive mask, so all you're left with is the person? At the heart of it, this is about automating the process of removing the same background from every image - so any alternate methods are welcome too. Thanks in advance!