I can't be sure if that's what happening here, but please bear in mind, that when linking binaries into a static library, its external dependencies do not necessarily get embedded into it, that means you might need to provide thet static libraries on which your program indirectly depends through libarchive, namely LZMA, zlib and bzip2 in your case, explicitly.
Furthermore there's some confusion on windows when it comes to linking static vs dynamic, for in both cases you provide a .lib file, so it is very easy to mix things up and provide the dynamicaly linked .lib, instead of the static version. If you do that, the linker may refuse to link your program (that notably happens with boost), or may link just fine and then, at the time of execution, the OS will require the respective .dll's.