It it possible to create a sort of pseudo freeze frame effect in post production on ordinary video or archival footage. For example, doing this in After Effects?
Yes it is. The idea is rather simple - you want to create a parallax effect.
Basically you take an object of interest in the foreground and roto/mask the object/person out.
You then duplicate that layer and reverse the mask for the background. At this point it should look exactly as it did at the beginning.
Now what you do is turn the layers into 3d objects. Position the background far away in 3d space, and scale it up so that it matches with the foreground layer as it did during Step 2.
Now create a camera and you can pan slightly and zoom to create the desired effect. Note that this may take some playing around, perhaps by scaling the background or the foreground layers more so that there is no clear 'space' between them.
If you want to do this with moving footage I would say it's probably not worth it as you'd have to do a lot of roto. But assuming you just want to do this with a freeze frame, it shouldn't take you that long.
Site note: usually what sells this effect is if you have something else moving really really slowly with the still frame grabs. Such as a 3d object you can manipulate in space. See this.