It depends on the device, and what you mean by "2.xx". Do you want A: stock Android? B: a ROM? C: a manufacturer-skinned stock image?
I'm going to assume that the answer do the question above is D: Any of the above. I'm also going to assume that by "2.xx", you mean 2.3. There are a few general requirements that will need to be fulfilled for it to be practical, and remember that this depends on the device and software; do your research before buying (assuming you haven't bought already).
1: The device was launched with Android 2.3 or earlier.
2: The device has an unlocked, unencrypted (or unlockable) bootloader.
3: (Pseudo-requirement) The device had, at the time that Android 2.3 was still important, an active development community.
If you meet the requirements:
You will have to do some google searching for various solutions. If you want...
A stock device image (not stock/"pure" Android) then you can find instructions generally by searching "unroot [device name]" on Google and XDA Developers.
A ROM: Go to XDA Developers or the popular dev community site for the device (Google is your friend) and search for CyanogenMod 7, or any other 2.3 ROM.
Stock Android: Good luck. I don't think you'll be able to find any flashable images with stock Android 2.3 for non-nexus devices.