Have experienced a similar situation; notified procedure had the fix at 5 dme 1600'Alt. When radar vectored, the a/c were at 2500' Alt before being descended to 1600' by the radar controller. Procedurally, planes levelled at 2000' ALt for terrain clearance until established, then when within 10 dme of the airfield, descending to 1600' Alt before the fix.
I never had a pilot descend from 2500' to 1600' without clearance but this was radar control service within class D airspace in the UK.
The answers will vary from country to country, control or advisory service, airspace type.