When set within an SBX, any files opened subsequently within that SBX will be auto-closed when this SBX returns. The flag name comes from the idea that in some kinds of menu architectures, you may use SBXs to execute programs that might otherwise have been executed with RUN. The difference is that in the case of a RUN, on exit, all files (and most other resources) are automatically closed or released, whereas with SBXs, files opened in the SBX remain open and accessible to the parent, as well as to other SBXs called by the parent or by the original SBX.
By setting the AF_SBXASRUN flag at the start of an SBX, A-Shell will automatically close any files that are still open when the SBX returns, provided that they were opened by this SBX (and after the AF_SBXASRUN flag was set). Files that were opened previously, and files that were opened by lower-level SBXs are not affected. (The case of the lower-level SBXs is under review and will probably be changed in a subsequent update so that those would be closed when the current SBX returns.)