Question downloads ever "disappear"?

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I know this is a very paranoid question, but I'd rather ask a stupid question and get a straight answer from a computer technician or someone who's had years of experience using computers rather than to keep wondering "what if."

So, is it possible for a download to ever "disappear." The reason why I'm asking this is because youtube keeps notifying me that they're going to stop supporting Safari (the web browser I use) and that I should upgrade to a more update browser. I use youtube to download a lot of videos. So I'm just curious if this is possible. Can downloads ever "disappear" or is it possible for my video downloads to not function properly in the future now that youtube has stopped supporting Safari. Again, I realize how paranoid this question. Have a good laugh, but answer with complete honesty.