How was I able to buy an app with no money in debit card account?

I was able to purchase a $1.99 app with $0.39 in my pre-paid debit card account that is linked to my Apple id. When they process the billing will they just delete the app from my phone or will I get some crazy fee on my phone bill for it?

No, they'll disable your account. Contact iTunes support:
http://www.apple.com/support/itunes/
They might even send these guys after you:

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