No, a PNG file is flat. The only way to get the background image without the working file is recreating the background image. You might be able to salvage some of the design if there is no image/text over parts of the background by using the pen tool or another selection method.
I think Fireworks is able to read layered PNG files if the original PNG was exported such in Fireworks. See How to read Fireworks PNG multilayer files without Fireworks
PNG files do not have layers, so Fireworks layers are stored in the
private chunks of the PNG files in a proprietary format which is not
PNG. I don't know of any program that can read them. You'll need to
ask the owner of these photos to convert them to flattened png
(mono-layer) or into another multi-layered format such as psd.
Answered by harrymc