The answer depends on the type of debt and the state and federal laws, if any that regulate it. For the most part, there isn't any set time period in the law for sending a bill. Getting a bill simply tells you that the sender is claiming you owe them $X and wants payment of it. For private debts (those not involving the government) the person claiming the money must sue you in court and get a judgment for what is owed, or, if there is an arbitration provision the contract between the parties, the claimant must initiate the abitration proceedings and get a decision in their favor before the they may actually start taking any assets to collect. (The big exception here is for secured debt like a mortgage or auto loan in which the property is put up as security for the loan). There is a limit on how long the creditor may wait before filing the lawsuit/arbitration claim, known as the statute of limitations (SOL). In Ohio that is six years from the date the debt was incurred.
It is irritating, of course, to get a late bill. I've experienced that myself. But if I owe it, I pay it anyway unless the SOL has run out for the creditor to get a judgment for it. There isn't any benefit to me in waiting further. Generally waiting to pay it any further simply makes things worse because the longer the debt is outstanding the more I may owe if interest and/or late payment fees are getting tacked on and the longer the debt remains outstanding, the more damage it will due to my credit rating.