Run the code in a "jail" or similar sandbox environment that enforces strict boundaries between the process and the operating system. This may effectively restrict which files can be accessed in a particular directory or which commands can be executed by the software.
OS-level examples include the Unix chroot jail, AppArmor, and SELinux. In general, managed code may provide some protection. For example, java.io.FilePermission in the Java SecurityManager allows the software to specify restrictions on file operations.
This may not be a feasible solution, and it only limits the impact to the operating system; the rest of the application may still be subject to compromise.
Be careful to avoid CWE-243 and other weaknesses related to jails.