In general, refurbished phones are sold independently from phone plans and contracts. Professional refurbishers tend to work on devices only (i.e. they're not carriers). That being said, you could find a refurbished iPhone that comes with a SIM card, so be sure to read thoroughly the information provided by the merchant.
If you already have a SIM card and a phone plan, make sure you buy a phone that is either compatible with your carrier or unlocked (meaning that it will work with any provider).