I believe it's more likely that they would sell out than be removed from sale. Even if someone originating from that departure point doesn't have the advance purchase period needed to buy an AP fare, there can be someone else halfway through their journey changing their return who would book into a booking class that is no longer available for new bookings.
Looking at fares filed for LHR-DXB, there are WTP fares with 7 days AP required (already too late to buy) and some CW fares that need 3 days. Most WT fares have no AP required at all.