Are there subsets of C that avoid compiler bugs?
blog.regehr.org
blog.regehr.org
http://compcert.inria.fr/compcert-C.html#subset
In any other case, the answer is almost certainly no. Most commonly used C compilers are sufficiently large and complicated that the chances of avoiding a compiler bug with a sufficiently large codebase is close to zero.
I already posted on Clight & CompCert which is much more salient in terms of ensuring compiler correctness and a safe subset that falls within the scope of the verified compiler's correctness.
Certified compilers are protected only by maintenance agreements.
When a piece of software is verified with an Agda proof, that is generally a real proof. The proof may not cover all aspects, but in those aspects you really do not have bugs.
Perhaps you mean non-proven certification? Or a weak certification of too few aspects?