Free to play games, what happens when they have paid dlc and they get removed from steam?

Interesting question . I also want to find out the answer ...

If a game is removed from Steam that requires connection to the internet to play. I would say most likely yes. This would be because updates for most MMOs or Massively Multiplayer games require security updates and patches that would otherwise not be given to Steam itself. If the game is a standalone free to play module; I would say you might be able to keep said game in most circumstances.

In the past you were able to bind F2P games to your account by these ways:
key activation
gift activation
purchased DLC

After the delisting game keys and gifts worked, but also DLCs which include the base game (you need to check the package on SteamDB for that).

BUT ...

The way F2P games are tied to your account/library have been changed (in the end of 2020 if I recall right). You don't lose them anymore by deinstalling. You can test that easily by deinstalling a still available F2P game and search your library afterwards. I have thousands of uninstalled F2P games/apps in my library right now.
The only reason to still prefer a key or gift activation is the +1 on your game count (if the game isn't profile features limited or the restriction gets lifted someday in the future).
Or if Valve changes the way all out of a sudden again ...

And - though it should be obvious - many F2P multiplayer games work only online and might not be playable after delisting, since servers are shut down, too.

For example I used to play a lot Marvel Heroes and bought a couple of bundles, game is still on my Library and I can check the DLC even their CD keys. I can download the game too but it would just never be able to log in into the non existant servers.

My guess thats what happens but dont know if it varies with other F2P games.