How can I check to see if a phone has an installment balance before purchasing?

Obviously, i am not a customer of the original carrier.

Please try again and explain more completely what you mean.

I think this is referring to buying a used phone. If it is still under contract with the original provider, the new owner may not be able to activate it. A common scenario is that someone signs up for a 2 year contract and gets a free phone and then sells the phone before the term is up. The new owner will have issues trying to activate it.

You want to check if the IMEI is clean. You can call the original provider and they can tell you if the phone is off contract or not. There are also some websites out there which can do the same thing. The IMEI is the internal phone serial number, typically shown on a sticker under the battery or in the phone settings screen.

Yes, there must be some website that tells non-customers this info.
Q: When is my device eligible for unlocking?
Your postpaid device is eligible to be unlocked by a participating provider after you have fulfilled the applicable service contract, completed the device installment plan or paid an early termination fee. Your prepaid device is eligible to be unlocked by a participating provider no later than one year after activation, consistent with reasonable time, payment, or usage requirements.