Yes, a landlord can try and collect money owed to him or her by a tenant even though the amount is 16 months past due. In most states, the statute of limitations for breach of a written contract is 4 years. The statute of limitations for breach of an oral agreement is 2 years.From what you have written, the time period to bring a lawsuit against you for money that is 16 months past due would not be barred by the statute of limitations.