The same problem exists at the function level: see bpo-39805: "Copying functions doesn't actually copy them".

For example, copy.deepcopy(func) returns func unchanged if it's a function.

Example:
---
import copy

def make_closure():
    closure = []
    def append(value):
        closure.append(value)
    return append, closure

func, closure = make_closure()
func(1)
func2 = copy.deepcopy(func)
func2(2)
print(func2 is func)
print(closure)
---

Output:
---
True
[1, 2]
---