Exactly how the mot man described it.If there's smoke coming out the tail pipe on something with a DPF, then the DPF has failed.
It's a filter, so it should not let any smoke through, regardless of how much smoke is coming out the engine.
The only time it's allowable to smoke, is during a regen, but it shouldn't be doing that for such a prolonged period it fails two emissions tests, and it's a totally different smelling/looking smoke than normal diesel exhaust fumes, so any reasonably competent tester should be able to tell the difference.