I got the following reply from Braintree support about this issue:
Because our sandbox environment is meant to replicate our production environment there is no way to force a subscription to past due. However here is a little work around that might make this testing easier:
To put a subscription in the Past Due status in the Sandbox, you can create a subscription with a trial period of one day and a price of $2000. Then, when the one day trial expires, it will trigger a transaction create that will fail because of the dollar amount.
The $2000 price tag is likely for the Test Amounts for Unsuccessful Transactions to trigger the credit card payment to fail. I have setup a test, and will edit this if the test proves unsuccessful.