It is common in Medication Assisted Treatment programs to screen patients for benzodiazepines. However, all doctors are as responsible as others, and there will be cases in which a doctor prescribes you both suboxone and a benzodiazepine at the same time. It is also possible that a patient will be prescribed suboxone by a specialized treatment facility and a course of benzodiazepines by their regular physician.
However, it is important to note that it is highly recommended that you do not mix suboxone and benzodiazepines. Because suboxone contains buprenorphine, a partial opioid agonist, one of its side effects is to depress the central nervous system, causing your natural breathing to slow down. Benzodiazepines such as Xanax or valium have a similar effect, slowing down your regular breathing cycle. Taken alone, your doctor or MAT nurse will be able to account for this respiratory depression by giving you a safe dose of suboxone or benzodiazepines. However, when you put the two together it is much harder to determine what constitutes a safe dose. This puts you at increased risk of losing consciousness, brain injury or even overdose.
Similar risks are associated with combining opioids and alcohol, as well as a host of other prescription drugs, so it is always best to seek medical advice before taking a course of opioids with any other form of medication. If you are receiving benzodiazepines for anxiety issues then there is a good chance that you will be able to seek out alternative medication or non-medicinal care pathways.