Functions and triggers allow users to insert code into the backend server that other users may execute unintentionally. Hence, both mechanisms permit users to "Trojan horse" others with relative ease. The only real protection is tight control over who can define functions.
Functions run inside the backend server process with the operating system permissions of the database server daemon. If the programming language used for the function allows unchecked memory accesses, it is possible to change the server's internal data structures. Hence, among many other things, such functions can circumvent any system access controls. Function languages that allow such access are considered "untrusted", and PostgreSQL allows only superusers to create functions written in those languages.