Copper wire has a few distinct properties; once it's bent, it stays that way, and it's really hard to take any bends out of it.
The only way to make copper wire flexible again is through the process of annealing it, which is just a fancy way of saying, heating it up.
Annealing copper wire is not difficult; you'll need a bit of newspaper or other light weight paper, and a safe place (outside, preferably) out of the wind.
Wind the paper around several pieces of reclaimed copper wire - this is the kind that is used for household wiring, usually with a coating of some kind of insulation, and a rubbery plastic sheath. This can be peeled off, like a banana peel with care.
So, now your wire is wrapped in paper, set the paper on fire. Use appropriate caution, such as having a fire extinguisher handy, or a bucket of water.
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Once the paper is burned off, the wire is now annealed, and will
remain flexible until it is once again bent. This process can be used
multiple times on the same piece of wire with no ill effects.
Carefully wind the wire around a spool; once you bend it, it again will stiffen up, so gentle persuasion is best.
Now what do you use your annealed copper wire for?
This is an important part of making bonsai, those tiny little trees in the Japanese style, for winding around twig brooms, hanging up almost anything in your garden, because, yes, copper wire will get verdigris on it which is a pale blue green tarnish.