Is there software that works without ECC RAM ? I think most popular databases just assume memory never corrupts .

I'm pretty sure they keep internal internal checksums at various points to make sure the data on disk is intact - so does the filesystem, I think they can catch when memory corruption occurs, and can roll back to a consistent state (you still get some data loss).

But imo, systems like these (like the ones handling bank transaction), should have a degree of resiliency to this kind of failure, as any hw or sw problem can cause something similar.