I found a recipe on my BigOven app that uses stand up/alone cupcake cups. I never heard of these. Could it be the foil ones by any chance?
My grandmother use to bake muffins and cupcakes in just the paper cupcake/muffin cups set on a cookie sheet. She would double them and use 2 paper cups per muffin. Sometimes they came out a little oval shaped, however. ;-) But it does work.
Foil cups have been used that way for a long time - it works better, IME, to line the foil one with a paper one. The foil cups tear into tiny shreds when you try to peel them off. For somewhat larger cupcakes, small ramekins of ceramic or glass can be used. There are also individual silicone cups that are made to be used for both baking and mis-en-place. .
I bought a set of those individual silicone cups that resemble the cupcake papers. Those things are terrible. The silicone sticks to the muffin or cupcake and tends to pull it apart. I would not recommend them. The paper liners are better and stick less, in my experience, even though they are not reusable.
I just bought a pack of CupcakeCreations® "superior quality heavy duty baking cups", because they were on sale for 25¢(and had a snowflake design) and the pack also states "no muffin pans needed". I had never seen them before and didn't know such a thing existed.
Made in Sweden, packed in USA; meets European and FDA safety standards; www.createcupcakes.com on the package.