Reland "Delay call to Destroy until after SignalDone has finished firing."

This is a reland of c7b8da453c2776a3e80fca3ff2400831adad03af

Original change's description:
> Delay call to Destroy until after SignalDone has finished firing.
> 
> Bug: chromium:905542
> Change-Id: I0def33a3ac21bd0da4b77ef05d42a0e7ef66caec
> Reviewed-on: https://webrtc-review.googlesource.com/c/112163
> Commit-Queue: Zach Stein <zstein@webrtc.org>
> Reviewed-by: Qingsi Wang <qingsi@webrtc.org>
> Cr-Commit-Position: refs/heads/master@{#25807}

Bug: chromium:905542
Change-Id: I5dd861bcd3b2ebcb7ff3db0888da1520eaaaca72
Reviewed-on: https://webrtc-review.googlesource.com/c/112240
Reviewed-by: Qingsi Wang <qingsi@webrtc.org>
Commit-Queue: Zach Stein <zstein@webrtc.org>
Cr-Commit-Position: refs/heads/master@{#25812}