Yes you can keep your old auto parts that come from an auto repair.
When an auto repair shop repairs your vehicle and they replace car parts you can request that they give you your old parts as a way to know for sure they replaced the parts.
Most of my customers don't want the old parts back but if they do I gladly give them the parts back.
Some parts have a core which gets refunded to the customer when they return the old part to the parts store.
Some people buy the parts and bring them to me and then request the old core part back and I gladly give them the core part back.
I also keep the old parts and show them the old part that needed replacing and some people don't want them back while other people do.
If they don't want the old part back it goes into a metal barrel and then is hauled to the scrap yard to recycle.
An honest auto shop or auto mechanic will gladly show you the old part or give it to you when requested.