A debt collector can take you to court and sue you over the debt if they do so before the statute of limitations is up.
The statute of limitations for collecting a debt are from 4 to 7 years depending on the state you're in.
In most states a debt collector has up to 7 years to collect a debt and if they haven't sued you for the debt then they can no longer legally force you to pay the debt or take you to court and sue you for the debt.
That doesn't meant that the debt collector will give up on collecting the debt but it means that the debt collector will be unable to sue you in court or legally force you to pay the debt.