I had a tenant try that. What happened was she wasn't going to pay at all..she figured I would take it from her deposit. I explained to her that she owed the rent..and that having an eviction on her record would be really bad for the future.
I served her with a 3 day notice. And, the day before court..she paid the full rent, late fee, and legal costs.
In New York, I can get a tenant out before the 20th...so..she knew that she was going to be living a few days in the truck if she didn't pay it.