Thank you! Would you bother sending a “prove the debt” letter to try and get the whole claim dropped (if they have nothing)?
Would prefer it gone, rather than just ignoring it!
Unfortunately a very naive attitude and gives the suggestion to the debt collector that you are indeed ripe for the picking off the gullible tree. By contacting a third party that has zero skin in the game and operate on a no-win, no-fee basis for their client as a scare tactic to pester you into paying something that you are not liable for and they have no contractual connection to, simply marks you as a "mug".
By contacting them, you can guarantee, 100%, that this not only won't simply "go away" but will result in even more harassment and communication. If that is what you want, so be it.
By ignoring it and getting on with your life, you win. They will eventually tire of sending you letters and will move on in search of lower hanging fruit to puck off the gullible tree. You have nothing to worry about so stop worrying and enjoy the fact that t is costing them to send you all the comms which you put to good use as emergency toilet paper, or whatever.
The advice "IGNORE" is your best guarantee that this will go away. Ignore that advice and you can guarantee that it will persist for much longer and they will find other excuses to chase you as you will not be marked as a "mug" ripe for picking.