I work for a West African airline and I can assure you that what you understand and what some of the Pilots understand is a world apart. Look at the callsign (or the transponder code given - which in our case is always 77??) The clue is in the transponder code.
If in doubt make it clear to the aircraft that they will take up the hold at BIG (or whatever). Do not expect the aircraft to auomatiacally take up the hold - despite no onward clearance. The magenta line flows from Biggin onwards and that is what, in some cases, you should expect the aircraft to do.