Killing a process when some other process is finished

Given a | b, i'd like to kill b when a is finished. b is an interactive process, which doesn't terminates when a is finished (fzf in my case), and the whole a | b is executed in a $() subshell. So far what i come up with was echo $({ sleep 5 & a=$!; { wait $a; kill $b; } } | { fzf & b=$!; }) sleep represents a, and fzf represents b, the result in the example is used by echo, but in my case, it'd be an argument for ssh. It seems, that $b is not the PID of fzf, it's empty. As far as i understand, this shouldn't be the case, since i've used {}, and not (), so it's not executed in a subshell.