I don't know which emulators do what but it is more of a function of the way the hardware is set up.
The SNES and most things newer than it have layers to build up backgrounds, text, sprites and such into a full image. For example the GBA and DS take this to fairly serious levels in their respective hardware ( http://problemkaputt.de/gbatek.htm#dsvideo
). I mention those for while you say 16 bit I should note that it and the saturn are basically where 2d went to shine before it all went software.
If you are emulating them it is easy to enable and disable them from your final render, indeed some emulators on less powerful systems fail to do layers properly (the SNES stuff on the GBA being a good example) and might have even had the option to switch the orders around.
Even without that most systems differentiated between sprites and backgrounds so you could usually disable those to get the backgrounds.
More hackery approach though if needed.
Most systems will support transparency/alpha in one way or another. You could then paint over the sprites/UI with the transparent colour for that system/palette.
Only real problem (other than not being able to see to play) is some systems use the sprites for hit detection. It is not a great way of doing things so newer systems dropped that method in favour of others but it is worth keeping in mind.
Even more hackery approach.
We tend to use the method for input mods and some aspects of sound hacking but depending upon the system it could work for graphics too.
If you read hardware docs most things on the system are controlled with "registers" (not to be confused with the CPU registers, though at times they can function in similar ways). If you can reach out and touch those registers with a cheat or with a simple assembly mod you can basically disable layers and sprites "in hardware"