yes there's a trace, and there's utilities you can use to "undelete it," but only if you do that "undelete" very soon after you've deleted it
when you do an ordinary delete stuff on one of these computers, the space on the storage device that file was sitting on, is not actually erased or overwritten, at least not right away
it's more like this. the operating system keeps track of all the available storage space on that device, with like a list. when you create a file, the os goes to its list and assigns some space on the device for that file to sit in, and then it's written there
but when you delete that file, the os just goes to its list, and marks the space that the file is sitting on, as "empty" or "available." it doesn't actually take the time to wipe that piece of space. the file is actually still there, you just can't see it
but the space the file is sitting in, is now listed as available by the os. if you create a new file now, the os could very easily assign all or part of the space of the deleted file, to the new file. the more new files you make, the greater the chance this has happened. and once it's happened.... you're not getting that file back, or at least not the whole file, and probably none of it.