The bug is that a 'damaged' anvil from 1.12.2, serialized as an Itemstack using ItemStack#serialize(); does not properly deserialize in 1.13 using ItemStack.deserialize(args) using a map with the same contents.

Reproduction steps.

1. Note that given a Slightly Damaged Anvil in 1.12.2, its corresponding Material Enum is ANVIL and has a damage value of 1. As a result, using ItemStack#serialize() returns a map with 2 entries. <"type", "ANVIL"> and <"damage", 1>.
2. In a plugin running 1.13, create/obtain a map containing the above two entries. Then using ItemStack.deserialize(map). It returns a plain anvil item. Not the damaged variety that is desired. I expect to get a "CHIPPED_ANVIL"

I have included a very simple plugin example showing the proof of concept. Hacking in a command "/getanvil". Which creates the above mentioned map and deserializing. The item placed in the player inventory is a normal Anvil.
Other flattened materials do not have this issue, just an anomaly with anvils.

The only other item I am suspicious about, is white beds. Colored beds were added in 1.12 where beds were converted to Red beds (?damage value 14?). I witnessed a white bed get converted to a red bed during my 1.12->1.13 conversion. But I have not extensively tested that part to see if it is suffering the same issue as these anvils.

Below is the disclosure statement that I read and understand. This is a bug with the Bukkit API, no concept of Vanilla testing is appropriate as normal world conversion seems fine.

PPS: Bug reports which do not 1) contain a declaration of testing in Vanilla and without plugins, or 2) in the case of plugin API bugs, contain a minimal reproduction case (source + jar please) will be closed. Bug reports must contain step by step instructions to reproduce the bug from a clean server install with no assumptions or prior knowledge. Also make sure you include the full output of /version in your report. Please copy and paste this statement to the bottom of your report to indicate that you have read and understood it.