That's exactly what happened to me & my gf (now wife) about 10 years ago.

We were paying month-to-month and I completely forgot to pay my half once. We were both super busy, I had just started a new job, my wife went back to school, etc. I didn't notice until a few months later. The landlord never asked for it, so I never said anything.

When we moved out several months later, the landlord must have done some final auditing or accounting and realized we owed that half month's rent. He came asking for it and we agreed he could take it from my security deposit so it worked out.