In short, no!
A contract is something you have to willingly sign up for/to. As such, when you first sign up with a supplier onto a fixed rate deal for a period of time, then the contracted period is the one you signed up for.
At the end of this, the supplier may offer you the ability to fix your rates again for another fixed term, but you do not have to. If you choose not to, you will instead be moved onto their "variable" rates.
Variable rates are exactly that, they vary, depending on what the supplier chooses to charge. Typically, these prices are higher than the "fixed term" deals, hence why people advise to sign up for a fixed period, so you know what you are going to be paying.
In short, a contract is agreed between the supplier and yourself. You cannot be signed up for a new contract automatically and especially not without your approval.