When the first of a model airliner is scrapped, the parts are worth a lot more money then the airplane is worth. As more and more of the model are retired and parted out, the value of those parts diminish.
Parts for a 727, DC-9, DC-10 or L-1011's are not worth much anymore, including engines so they are just scrapped for the salvage value of the metals when they are phased out.
757 and 767s parts are worth a lot of money now so you will are now seeing some of the early older models being parted out when they run out of airframe time for the next major inspection.
Some models, like the 747's have so many variations and different engines that some models are worth more than others for parts.
In some cases as the airlines slowly retire their airplanes, they use the parts from the retired ones to support the remaining in service airplanes. It is a lot cheaper to reuse low or mid time engines and components than to overhaul them.