Generally, yes a tenant has a right to cure the default (i.e. pay all rent due) up until the court enters an order or writ of possession for the landlord. Entry of such an order will usually happen at the hearing or shortly thereafter. You should make payment of the back rent as soon as possible, and make sure there is a record of the payment (certified mail, cancelled check, etc). Then appear at the hearing and defend against the eviction on the basis that the landlord has already been paid everything she is owed.
You may want to consult with a landlord/tenant lawyer in your area.
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