How do compilers assure stability?
It happens that compilers contain subtle errors. No blatant errors, because blatant errors would be detected and fixed.
A compiler that is itself compiled by a compiler with subtle errors will tend to have blatant errors. They will be easy to detect because they are so blatant. They will be hard to fix because these blatant errors will be produced by perfectly fine source code, so whoever wants to fix it will have a hard time finding the real problem.
The solution will be to make a compiler of sufficient quality that bugs are very rare, and extremely rare within the compiler. We also expect compiler bugs to affect very complicated code more, so the compiler writer should write code that is simple and follows common coding patterns.