I used to work for a company that made the metal-cased ones, like this:-
https://uk.rs-online.com/web/p/crystal-oscillators/7960520
We bought the bases and added the crystals, adjusted the frequency and welded the lid on. It allowed custom frequencies is a couple of days.
Anyhow, we very, very rarely saw problem with the oscillator part, which was really simple anyhow. It was a couple of transistors, or a couple of inverters. There were also some that had dividers in them.
The ones we made had decoupling capacitors across the supply, but I am not sure if the plastic ones have those. I know that the small ceramic ones tend not to contain decoupling capacitors.
The failures were generally the crystals. They could lose activity, which effectively meant that they went open circuit, or they could break and go short circuit, but it didn't make much difference to the behaviour in that most designs without dividers would end up with the output at mid voltage and the oscillator taking quite a lot of current, more than it did when working properly.
The crystals that we used were circular, so the orientation was random. Crystals in the 4 - 80 MHz range are called AT-cut, with those above about 30 MHz being run in third-overtone mode. The cut of the crystal is the angle which the disk of quartz is cut from the single crystal of quartz that has been grown in an autoclave. The angle affects how the frequency changes with temperature, and there is only a narrow range of angles that is used to keep the frequency stable.
AT-cut crystals oscillate in thickness-shear mode, like a jelly wobbling side to side. The direction of oscillation isn't important in a circular crystal, but in the plastic oscillators, the crystal is inside a cylindrical metal can, like a watch crystal, and the rectangular crystals have to be cut so that they oscillate along their length, or they would not oscillate properly.
I don't think that the orientation of the crystals can vary inside the plastic oscillators. However there are lots of other ways that crystals can be made badly so that they fail prematurely. If the crystals aren't properly cleaned before the electrodes are added, or the silver electrode material is added when there is not enough vacuum, the electrodes can come detached. If the crystals are chipped or cracked, the cracks can grow until the crystal fails. The metal cans are welded, but if that isn't done correctly, oxygen can get in and corrode the electrode.