An exhaust back box can easily last over 50,000 miles, it will normally depend on a number of factors how long exactly it will last. As the exhaust, being mounted underneath the car, is always exposed to the elements the climate you drive in as well as the type of roads that you drive on can impact how quickly the deteriorates. The exhaust back box can start to corrode in a wet country like the UK. Furthermore the overall condition of the exhaust can also have an impact on how the back box deteriorates. Making sure therefore that the whole exhaust system is in a good condition can help extend the lifespan of the various individual parts.
It's important to get any issues with the exhaust fixed before you drive the car again therefore.