1. You mean just BEGIN, not sub BEGIN. You're also missing a semicolon after package foo.
2. You should be naming your package files with extension .pm, not .pl. You also don't need to specify the extension when require- or use-ing.
3. You define subroutine in package foo, but try to use the subroutine from package1.
4. The biggest one: The behaviour you describe has nothing to do with BEGIN. It works just the same if you remove the BEGIN {} block.

UPDATE: AnomalousMonk points out (indirectly) that my point (4) is “only just” correct—the very early initialisation provided by BEGIN {} can certainly be useful if you might call a subroutine before some variables in it would be initialised by the normal flow of code.