Fonts disappearing is not a big issue that will ultimately render your page useless. If the font is gone, the look of the page is slightly affected, but the content of the page remains. It's honestly not a big deal at all.
Here as we enter the 2020s, there are no longer any web safe fonts. Those 1990s Core Fonts for the Web (Verdana, Georgia, Trebuchet, etc.) are no longer universal across all widely used platforms.
Yeah okay, but the initial suggestion (just specify "sans serif") still holds. Or really, if we're talking about a webpage to last, why do we even care about what font is being used? If you care enough about a font that the glyphs used are important for layout, then obviously you're going to need to include the font. If the specific look of the page is essential to the content conveyed, it seems likely to me you won't be using a standard font anyway.
For typical "the words matter more than how the words look" content...can someone explain to me why we care about including the font?
There’s also layout issues caused when replacing a font with another font, unless the metrics are precisely duplicated. There’s a reason RedHat paid a lot of money to have Liberation Sans with the exact same metrics as Arial, Liberation Serif have the same metrics as Times New Roman, and Liberation Mono have the same metrics as Courier New.