I keep reading things like “smallpox has been eradicated” or “there are only two samples of the virus left in existence in a lab somewhere”, but couldn’t there be a bunch of smallpox viruses in an alleyway where some infected person sneezed years ago? Is there some reason the virus can’t exist without a human host?
The viruses that caused smallpox (Variola major and Variola minor) are generally not stable in the environment (<24 hours as an aerosol), though they may persist for more than a decade within scabs Reviewed: Sinclair et. al., 2008 OSHA.
UV light is an excellent disinfectant, so typically any virus exposed to sunlight will lose rapidly infectiousness.
You may also find this answer to a related question of interest: https://biology.stackexchange.com/a/59165/46609