How to list only non-<defunct> processes?

In your comment you clarify:

I'm actually looking for a single step option to ps or pgrep (or similar) which only outputs "active" processes...

I'm afraid you're out of luck with current ps/pgrep implementations.

Post filtering like this relies on a full understanding of the intial output, which I don't have...

But you can get that understanding and, better yet, control that output as desired. Try something like this:

function pgrep_live {
  pids=$(pgrep "$1");
  [ "$pids" ] || return;
  ps -o s= -o pid= $pids | sed -n 's/^[^ZT][[:space:]]\+//p';
}

That will return the pids for any pgrep'd processes matching your input string, which processes are "available for normal use," that is, neither dead+unreaped (Z) nor stopped (T).