Depends upon the game and the system it is running on.
For 3d games on actual 3d hardware the most common start would be 16:9 rendering if the game started life as 4:3. Such things have even been done on hardware (the wii and the gamecube for instance). Terms like viewport rendering then want to come in and make a good jumping off point for a search.
Resolution wise it has long been done with emulators, there is even a DS emulator doing it for its 3d with spectacular results.https://gbatemp.net/threads/hi-resolution-ds-emulation.364549/
Textures look a bit iffy when you try upscaling, though such things are also not trivial for some systems as they can use odd ways of texturing, but high resolution texture replacement (or even texture addition if raw model colours are used) is also a thing emulators do, shader fiddling is also possible but not so many have engaged in this as far as hacking goes, for PC games it is quite common.
Couple the three together and you can change the camera location, increase the apparent resolution/rendering resolution of models (maybe even subsurf it once or twice more) and change the textures.
Systems built around 2d, including UI elements of the 3d stuff above, find all this considerably harder if the game in question is not an interpreted one (SCUMM, ZZT... something you can edit really). Background layers can be higher resolution than the screen itself (1024x1024 backgrounds are seen in some modes on the DS which has a 256x192 screen, well two of them stacked up) and even beyond that many systems/games will tend to have one extra tile at least in VRAM. However animations, enemy logic, scripted events, game logic, pop in..... is often defined by this, indeed the viewport rendering stuff in 3d can have similar problems even it is far easier to attempt to solve (not the most obvious flaws compared to some games but https://www.youtube.com/watch?v=YI1gHmgKmKo
showcases a few).
To that end unless the 2d game has some kind of zoom function you can abuse it is likely to be a crazy involved hack. Theoretically you could do some kind of enhanced border where you take a snapshot/savestate, move the camera/oam over by some, snapshot, repeat for the other directions and then staple that onto the original game that you have restored the savestate of. For some games it might work but you also might be triggering scripted events, enemies, something else entirely and then end up with some very odd looking. If you were playing a horror/psychological game then that would probably be a great effect actually (call it peripheral vision in an unsettled mind) but for most purposes it would be more of an enhanced border.
Edit. Forgot to mention that with higher resolution, or even in general, and 3d you can then sometimes also force the camera out further. Most camera forcing tends to be things like first person hacks or god view but the principle is the same. This sort of thing is probably obvious but I should mention it anyway.