Welcome to the community!
Most of the Canadian cellular providers offer subsidised plans. That is, the plans incorporate the phone subsidy into the small, medium, etc plans. At the end of your contract (or if you pay off the balance), the subsidy remains as a part of your plan should you wish to get another phone. You should note this system is different from financed plans offered by some providers of the US and Tabs (see here). With financed plans and Tabs, once your contract is finished, the financing and Tabs are also complete. Most Canadian providers do not use a finance model while a few only recently started to use the Tab model.
If you do not wish to subsidise another phone, you would need to switch to a current in-market Bring Your Own Phone (BYOP) plan. Current in-market plans may or may not offer the same details as your current plan. If you do not request to switch to a BYOP plan, your plan would remain the same as during your contract, though it would be on a monthly basis.
If you later decide you wish to subsidise a phone after switching to a BYOP plan, you would have to take a subsidised plan which is in-market at the time you decide to switch. Again, the plan details of that plan may or may not include the details of your previous subsidised plan (or 'current' BYOP plan).
In order to pay the remaining balance on your phone, you can go to your My Account --> Usage & Services --> Mobile --> Change Plan. If you select a BYOP plan while you have an agreement it will give you a little warning with regards to the amount you need to pay for the downgrade fee (see here).
Hope this helps