How would you handle this disaster? Redditor nerdy_J said a friend's kid did this to all the cans in the pantry. They were lucky that the labels were still there at all. Do you know what's in your cabinets well enough to figure out what's in the cans? Tomato paste, tomato sauce, corned beef, and tuna are pretty easy. I hope you store the cat food in a different place. Some folks at the post shared what they did back when they got unlabeled canned food free.
When I was a kid we were really poor and would volunteer to take food from local grocery stores to the local food pantry. Legally, the food pantry could not accept cans without labels, so rather than throwing them out we would take them home. We all got pretty good at guessing what was in a can by how it sounded when you shook it. We would also make “mystery can soup”. Basically get a cheap chunk of roast and then start opening cans: vegetables went in the soup, fruit went into a bowl for fruit salad and cat/dog food/mystery meat would go to the cats.
That plan gets a wrench thrown in when you open a can of tamales or chow mein, but those can be refrigerated for a while. I am reminded of a Girl Scout camp out where we all brought a can of our favorite soup and threw them all in a pot together. The real problem with your canned goods shelf is that you keep too much stuff around that you really don't want to eat. I once bought one can of French onion soup because I like it, but the hassle of preparing a couple of slices of French bread and melted cheese meant I never prepared it. Yesterday I checked and found the can expired four years ago!