SQLite is tested against failure to allocate at every step of its operation: running out of memory never causes it to fail in a serious way, eg data loss. It's far more robust than almost every other library.

Unfortunately it is not so easy. If rigorous tests at every step were able to guarantee that your program can't be exploited, we wouldn't need languages like Rust at all. But once you have a program in an unsafe language that is sufficiently complex, you will have memory corruption bugs. And once you have memory corruption bugs, you eventually will have code execution exploits. You might have to chain them more than in the good old days, but they will be there. SQLite even had single memory write bugs that allowed code execution which lay in the code for 20 years without anyone spotting them. Who knows how many hackers and three letter agencies had tapped into that by the time it was finally found by benevolent security researchers.