When the computer goes to sleep or suspend mode, the state of the OS and all the processes are stored in your PC's Random Access Memory (RAM)
What if the RAM (physical or virtual or both) are maxed out?
I think you misunderstood something. The OS and running processes are already in memory. Nothing gets loaded into RAM just for Sleep mode. Everything just stays as it is and RAM continues to be powered while sleeping.
With suspend to disk (hibernation (and hybrid sleep) everything in RAM is stored on the hard disk and the computer is powered down. But that's something else, of course.