There are various fixes for the dead zone problem.
In the mid-1970's, Fairchild (the original company)
sold an "11C44" phase detector that got rid of the
dead zone by injecting a narrow pulse so that the
phase detector pulses would never have to try to
go to zero width. Eric Breeze holds the patent
on this technique; if interested read his patent.
Analog Devices makes that AD9901 phase detector
which gets around the dead zone by first dividing
the frequency by 2. However, it is not suitable
for a frequency synthesizer because of the large
spurious sidebands resulting from this technique.
Motorola had some patents on the circuits in its
MC145159 that dealt with the dead zone and sampling
sidebands. It also used a divide by 2 technique, that
was not documented; (we figured it out by observing
the chip's output). That chip may have been inherited by
On Semiconductor. It was originally developed for
some division of GE.