Your options
Repayment plans in New York
A repayment plan usually means the regular payment plus an extra monthly amount until the arrears are caught up. It can work when the default is modest and the household income can genuinely absorb the temporary increase.
It is usually a weak fit when the missed payments are large, the hardship is still ongoing, or the extra monthly amount would only create a second default later.
The point is not to pick the option that sounds disciplined. It is to pick the option that can survive real life.
Trying to catch up without selling?
The payment math matters more than the label on the option.