Speaking to shrinkage and warpage of parts and eventual potential of stability, there are many process dependent factors; setting those aside, keep in mind that plastics, such as HDPE, when at room temperature are neither melted nor "frozen" (below the glass transition temperature), having both amorphous and crystalline constituents with some degree of molecular movement; eventually these constituents reach an equilibrium, where the amorphous and crystalline content percentage is stable. Injected, cast, pressed, or extruded parts- any that have been formed by heating above the melt point -on cooling will continue to shrink or warp to some degree until reaching that equilibrium point. How long does that take? In the case of HDPE, the last 2% of shrinkage may require up to 3 months to occur! HDPE may demonstrate 85% of shrinkage within 24 hours, 98% within a week, and that last 2% by 3 months.
What does that practically amount to? Say you injected a meter long beam, with a gross shrinkage of 3%, or 3 cm. A day after de-molding, shrinkage might be measured at 2.55 cm; at a week, 2.94 cm, and at 3 months 3 cm. (Yes, that last bit is just 0.6 mm change!) This is just an abstract example- many factors will impact the actual shrinkage rate, such as pressure, mold temperature, and annealing. Other plastics shrink far less, or stabilize over a shorter period, or in the presence of moisture.
While annealing time, temperature, and pressure contribute to total shrinkage, the increased density they may deliver also raise the glass transition temperature, shortening the distance to equilibrium.
The take-away for me is 1) know your plastic, 2) know the purpose of your plastic, 3) build in plastic "set" time, as appropriate. For those formulating an annealing strategy for stabilization, it may behoove them to incorporate the time required to reach equilibrium in the plan.