First, there is no jailbreak for Xbox360. It is either Jtag or RGH which are similar to what Jailbreak is but not teh same. Or there is a flashed optical disc drive that allows you to play burnt copies of Xbox 360 game discs. Or there is Xk3y which is a USB loader that fools the console into thinking the game is being read from the optical disc drive.
Do you know which one you have?
Whichever one it is, you can still use a HDD cloning app to clone the 80GB image over to a 500GB HDD. The 80GB will remain the same as it was before and at the time of cloning. The new 500GB HDD should be fine with the data from the 80GB and the extra 400+GB of space available for you to use, but there is always the small chance it might not work well with the Xbox 360 unless it’s a known highly compatible brand/model HDD.
I did something similar recently and used EaseUS HDD cloning app. There is a free trial that worked fine for the couple HDD drives I needed cloned over to SSD drives. I put SSDs in my 2 RGH’d 360’s just for the hell of it and they do seem a bit faster now when loading certain games up.
Hope this helps & Happy Holidays!