If it's factory unlocked Apple will not turn it off! the carrier will turn it off if you don't pay the bill. other carriers will see the fact you owe money and might deny you.
non factory unlocks Ultrasn0w involve certain firmware baseband and requires you fallow certain rules to keep/ (nothing to do with Apple)
Your carrier can still turn your phone off if you don't pay the bill.
Can I unlock Click Me!
No matter what you do, your carrier (And possibly even other carriers) will deny you service if you have not paid your bill. Regardless of if your phone is unlocked or not.
No, apple can't lock it back up. Just don't do a software-update from iTunes (You are free to sync and backup).
Unlock is defined as using a phone on a carrier that it is not originally sold for. Say, you unlock a phone on Orange, you could use it on O2, T-Mobile, etc. That is only if the carrier allows you to have service. If you don't pay your bill, the carrier will stop the service on their end to prevent you from accessing it, and at that point, no matter what you do (Other than pay your bill), you won't have service. Even if you unlock, you still have to pay your bill to your carrier each month.
EDIT: If your contract term is not finished yet, you are not allowed to leave them. If you can't pay, no matter what you do, you can't have a phone with service. I'm not familiar with Europe's way of handling things, but here in the US, you can pay an ETF (Early Termination Fee), and get out of your contract by paying ~$175 - $10 for every month into your contract.
If you can not afford to pay your monthly bill anymore, the best solution would be to tell your carrier to suspend your account. No matter what you do, you won't have service if you don't pay your bill.