Debt collectors can pursue the debt for as long as they want but there's a statue of limitations on how long they can legally pursue the debt and sue you in court for the debt.
They have up to 7 years to collect the debt or sue you in court for the debt and if they don't collect or sue you in the 7 years then when the 7 years is up then the debt collector will be unable to file a lawsuit against your for the debt owed and you legally no longer have to pay for the debt.