It's a difficult problem to troubleshoot. Everything is level-shifted, there's six different rails/bias voltages and VFD's are uncommon knowledge. A troubleshooting mistake is too costly for these gems.
The NEC MCU VFD driver stage could age and go leaky from ion migration on the die.
I thought this was the root cause of ghosting segments, but
xemax replaced the VFD which fixed the problem My understanding is OP disconnected a VFD segment from the driver IC and the segment remained lit, ghosting. He then added a very strong pull-down of 2k7 (to -18V? GND would not go to cutoff) before the segments went out. The driver MCU output stage has internal ~140k ohm pulldowns to -18V, there should be very little current in VFD cutoff. This implicated the VFD display as being leaky.
I do not know of any current-leakage path inside a VDF other than a gassy tube (partial air ingress), or stray capacitance causing ghosting due to mux frequency.
Measuring voltage (to GND) on a disconnected segment or digit control grid will give a -ve voltage reading, as electrons flow from the cathode to the anode or grid then multimeter (+). You can have grid current flow, it is not always high-impedance if near or above the anode potential.
This is the problem troubleshooting- if the VFD+driver IC pin stays too +ve and the segment ghosts, it could be the IC or the VFD it seems.
edit: fixed URL