It is better to give a formal resignation, collect the full and final dues, if any and move on (which I believe you already have since it has been more than a month).
You said you left the organization, does that mean, you absconded? I probably think you would have as you have mentioned leave of absence with intimation. Your employer can close the case by sending a show cause notice. You can as well send in your resignation now, but not sure what would be their motive in asking that after a month. Do you own any company owned properties with you?
According to me you should put down your paper as this will be a wise decision, as the termination letter carries a negative impact for the resume along with it, and where as employer is concerned he could have terminated you in your absence as that becomes absconding if no intimation by mail has been given stating the reason for leave. therefore it will be a mature decision to put your papers down instead of getting a termination letter.