The MRR calculation incorporates all invoiced recurring charges, credits and refunds from active subscriptions. You can tell whether or not a charge has been included in MRR if the line item associated with that charge has a start and end date on the invoice. Failing an invoice will not automatically remove it from your MRR calculations.
While we recommend that you "Keep all recurring charges in MRR", you do have the option of edit whether or not you wish to include recurring charges from failed invoices in the MRR calculation. With Analytics User permissions you can view this under the Configurations > Analytics Settings > MRR Settings > Failed Charges. Here you can select to "Remove failed recurring charges from MRR". Selecting this will remove failed recurring charges from your MRR calculations.
We have some more information on MRR in our docs here: https://docs.recurly.com/docs/monthly-recurring-revenue-report#section-monthly-recurring-revenue-mrr-