Even though it doesn't show in the output of `:display`, when you use the plus or star registers in TTS (i.e., a mode without clipboard feature), it stores the content in the `0` register. The code is in the [`get_yank_register`][1] function.

If we see the else condition, which is what gets executed in TTY mode for star and plus register (I double-checked with gdb), we'll see it sets the register being handled to 0.

```c
else		// not 0-9, a-z, A-Z or '-': use register 0
	i = 0;
```

The same is true when you're pasting the content (the argument `writing` is false in that case, everything else is the same).

Why the `0` register doesn't display it is still a mystery to me. I'll look around and update this answer if/when I find that answer.

[1]: https://github.com/vim/vim/blob/ee09fcc9b6cf24e02899461809da9a5148208ea5/src/register.c#L240-L259