EE's traditional contracts have no concept of paying off any phone - you agreed to pay your single monthly fee for at least the duration of your minimum term, but ultimately until you explicitly requested a change.
Towards the end of your minimum term, you should receive a text message advising of numerous options - one of which includes changing your plan to a SIM-only. Ultimately the choice needs to be yours, thus if no change is requested, none will be made. You are free to make this request anytime once your minimum-term has expired.
The newer FlexPay plans specifically structure into 2 separate contracts, each with their own payments. You have a (normally) 24month fixed-term finance loan, and a separate minimum-term based airtime plan - similar to a SIM-only.
