I had this problem too in 2016. I had been in that job for a couple years now, so I had a good record with them. Personally, I was up-front and they said they (odviously) could not let me work past the expiration date, but they would hold my position for a while. I received my renewal a month and a half later and went back to work.
The big question is, what's better...Them finding out? Or, you being up-front and telling them about it?