Is it possible the still fight in the arena after beating the last person or what will happen?

Yes. They can arrange weekly fights for you against varying creatures. :toughninja:

If you want more info on that, here is link: http://www.uesp.net/wiki/Oblivion:Arena_(faction)#As_the_Grand_Champion

There are also a few mods (for PC users) that add on to the end of the Arena quest by adding periodic challengers. I haven't used any of them myself, but I looked into them for inspiration when I added a Grand Champ's quest to my own mod - which also features a challenger, but she can't be killed!

I suspect that it would not be possible to run more than one of these mods at a time, so if you decide to try them, make sure each one can be un-installed after you're done with it without breaking your game. And if you only pick one, make it mine.