Can I keep downloaded games on a 3ds XL after a system delete?

December 2014

I decided to buy a Nintendo 3DS XL off of eBay, and found one with hard copies of games, and Ocarina of Time 3D installed onto the device, so when it arrived at first I was super happy as I had these games, but soon realized that I wanted to make the 3DS my own, by factory resetting it so I can create my own profile and change the settings to my choosing. However, I was told that by doing this it will delete the system installed games, as a game is linked with the previous owner's account or something. So long story short, I want to know if there is a way to keep these games after a factory reset. If there isn't a way then I wasted money on a game that I can't even keep.

Update - January 2015

I decided to perform a factory reset on my 3DS as I wanted a new NNID more than I wanted the downloaded games. I removed the SD card and began the process. After I did this I fully expected for the titles to no longer be on my 3DS. So I set it up, and they weren't there. No surprise there. But, I made an account on e-shop, and decided to check on the re-downloadable software thing, just in case the games happened to be there. AND THEY WERE! I downloaded them and they work perfectly fine! I have no idea how this happened! So so shocked, but happy. Can anyone explain why this happened? As the games should have been linked to the previous owner's NNID, so how did I get them back when I made my own NNID on a factory reset console?

According to Nintendo Support:

A Nintendo Network ID is required to download game demos and other free software.

Once deleted, Nintendo eShop purchases can be redownloaded at no cost. Downloaded items appear as a gift on the HOME Menu. Once they have fully downloaded, you can tap them to access the software.

What to Do:

1. From the HOME Menu, select the Nintendo eShop icon and tap "Open."
2. Scroll left and select "Settings / Other."
3. Scroll down and select "Redownloadable Software."
4. Select "Redownload" next to the software you wish to redownload.
5. Select "Download."
6. Select "Download Later" or "Download Now." Items downloaded now will begin immediately. Items downloaded later will begin when the system enters sleep mode.

TL;DR: You need the original Nintendo Network ID to redownload the previously downloaded softwares after a console format.

You can transfer data between two consoles before a console format, but that will transfer the Nintendo Network ID account, too. You cannot transfer data on a console with another Nintendo Network account.

You cannot perform a system transfer if the target system has a Nintendo Network ID linked. You must format the target system to remove the Nintendo Network ID link prior to transferring content.