Operating system: Windows-7-6.1.7601-SP1 64 Bits
Graphics card: GeForce GTX 980/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 425.31
Broken: version: 2.83 (sub 4), branch: master, commit date: 2020-02-18 09:10, hash: rB79f99becafa3
Short description of error
Symmetrize operator automatically disconnects bone parenting for "Bone.L" if "Bone.R" was connected to a non-mirror-bone, for example "Bone_root". I assume its intended to force the Bone to the other side.
But in a case where the parent bones end / root of the connected bone is exactly at 0 on the X-axes, it might be relevant to preserve the connection, as you can see in the picture.
Exact steps for others to reproduce the error