Figured I'd offer an update to this question so that it remains relevant:
Since the release of Mists of Pandaria in 2012 and its introduction of AoE looting, you can simply kite and kill another enemy close to the unlootable corpse and loot the enemy you just killed.
As Nzall has already pointed out, you can continue playing with the same characters after subscribing. From the website:
When you're ready to progress further, simply subscribe to access an
ever-growing universe and continue leveling to 50.
Note that you can only play characters over level 20 if you have an active subscription. If your subscription ends or ...