Since the kernel's memory is in each process address space, it is vulnerable to being changed by user space code. This is a security hole as well as making the entire virtual machine vulnerable to a badly written process. The one tricky aspect of this is that the code which write-enables kernel data will run on a kernel stack, which needs to be writable already. So, that stack page will be left writable when the process is running. It's not a problem if the process manages to modify it because it is fully initialized before any code starts running on it.
Nothing depends on anything left behind on the stack.