How does a web browser handle the case when a given glyph, character, symbol, dingbat, etc is missing from a font ? You can for example declare fonts in your CSS that don't include the font maker recreating: Unicode Character “⌚” (U+231A) yet it will still render. How does the browser make the decision itself?
So the font matching algorithm is relatively complex so I don't want summarize it incorrectly. But basically after it goes through the fonts mentioned in your CSS and none of them work it goes to a user agent defined system font fallback procedure. There is no spec or standard for this, so it is going to be browser / user agent specific.