In a recent support case I was asked to provide some solution about SER and Handling of soft errors.
We have a great AN about this subject and I am also providing a code example that goes with it. The code is for a STM32F072 and uses SRAM parity check to detect an error in the RAM and recovers from it (to some extent).
I have also attached a presentation about a special case: we worked to provide a solution on a recovery for issues related to unaligned memory access.
On M0 core it is hard to do any recovery since the information stored relative to execution are minimalist, M3 or M4 can provide more details, but it is complex to discard all potential reasons leading to an hard fault in order to recover. In the attach presentation and project we just develop a solution to check if hard fault was from unaligned memory access and recover from it then.
This will be useful for you if you want to add robustness to your application.