The answer to that question depends upon how you define “active”.
You can have a contract under which you may no longer make purchases or the supplier may no longer need to sell as the purchase term has expired. While the purchase term may have expired, those agreements will remain "active" until all contract obligations are met. If the term of the agreement has expired, that doesn’t excuse the buyer from making any payments that may be due. The supplier may have warranty obligations. The obligation that you want to survive the either the termination or expiration of the purchase term are normally spelled out in what’s called a survival clause. Survival clauses would include things like the responsibility to pay taxes that may be due based on the work performed or products delivered. The obligation to pay any amounts due and payable. The responsibility to repair, replace or correct any defects under the contract warranties. The obligations to defend against certain third party claims as provided for in any indemnification. As there may be law suits that happen after the expiration of the contract, you would also want any limitations of liability, the order of precedence and agreed choice of laws and forum for any disputes or agreed method of arbitration to survive. If the contract had confidentiality obligations included, you would also want those to survive.
Some of those surviving obligations will have a specific term after which they expire. For example warranties may have a specific duration after which the supplier no longer needs to honor the warranty. The obligation to maintain information as confidential usually has a term associated with that. Taxes and indemnifications will normally not include a specific term. So the contract is still “active” until those obligations expire. The thing that will cause the tax obligation to expire is when the applicable government can no longer make a claim for taxes. The thing that will cause the indemnifications to expire is determined by the statute of limitations for the specific jurisdiction. The statute of limitations places a time limitation upon when a suit may be brought and they will vary by jurisdiction. For example in New York the parties to a contract have six years in which to bring a contract claim including a claim for fraud. For claims of personal injury or product liability a third party has three years from the date of the injury in which to bring a claim. A claim of infringement of intellectual property rights normally has three years after the infringement should have been reasonably discovered by the owner in which to make the claim.
Since contracts are “active” until all obligations have been met, most companies will have a formal records retention program to retain the contract files until all potential claims that could be made have expired. They may not be active in terms of needing to manage them, but they still need to be retained. While a contract file in the U.S. may only need to be retained for seven years from a perspective of taxes, as a minimum you should retain it for at least the useful life of the product plus three years, if not longer. I’ve had many times where I had to call our records retention company to pull contracts that hadn’t been used in ten or more years.