BungeeForge is a Forge mod that implements BungeeCord (legacy) protocol.
At first it was developed to support Velocity legacy forwarding but it can also work for other Bungee proxies.

• Download the mod into mods/ directory on your server
• Setup Velocity (velocity.toml) option player-info-forwarding-mode to legacy
• Configure your Forge server (server.properties) option online-mode to false
• Connect through Velocity to your Forge server
• You should see skins and IP forwarding works

This modification requires both Proxy and Forge to be compatible. Unfortunately, currently, Forge for Minecraft 1.13 (and newer) is not compatible with proxies due to the lack of a "reset" packet to gracefully reset client registries between server switches. To implement this functionality, there is an available plugin called Ambassador which was thankfully developed by adde0109. Install both BungeeForge and Ambassador on 1.13+ setups. For Minecraft 1.12.2 and lower versions, BungeeForge works by itself.

Other Forge versions can be supported as well. Please feel free to create a Issue and ask.

Take a look at Void Proxy as alternative to BungeeCord and Velocity.