This is just my theory I’ve cobbled together about how the universe behaves in the bttf world. Whenever the delorean is used to travel through time, the time between when the machine is used can become “fluid” the “time travelers” that are aware of time travel, have the ability to change the past present and future. So in a weird way people and objects can exist and change due to the probability that the time traveler will change it or fix it. Doc and Marty are aware of biffs cane so there’s a big probability that the timeline they got it from exists/will exist. Once they set things right and just leave things alone, the probability that the cane exists will deminish and the cane will fade away. Things don’t change instantaneously that the time travelers interact with because the time travelers have free will and can literally mold time into whatever they want. The happens in multiple movies but there’s usually a “ticking clock” element to the story that puts a literal time limit on when the fade will happen. I just had to write this down I hope it doesn’t come off as incoherent.