See my before-last paragraph above: no, regarding hardware video acceleration, even Chrome doesn't do what you describe. What you describe stands for non-video content crashes, which isn't what's being discussed here. Could the technique you mention be applied to video gpu crashes? I personally don't know and I'd lean towards "nope" (else Mozilla & Google engineers wouldn't be so exceedingly cautious about it). If anyone is knowledgeable enough to precise / contradict this, please chime in.
At any rate, even Chrome is built with zero hardware video acceleration support on Linux (hardware acceleration yes, hardware video acceleration no). Chromium does offer the option, just as hidden behind flags as Firefox, and until last month you had to build it yourself with a VAAPI patch left unmerged for years by Chromium devs.
In the meantime, to save you rummaging around bugzilla, follow https://wiki.archlinux.org/index.php/Firefox#Hardware_video_... , it's the most constantly {up-to-date, concise, reliable} source you'll find. You don't have to be using Arch, the information contained in this section applies to any Linux/Firefox distro.
Note that Firefox isn't the only browser to struggle with it; see https://wiki.archlinux.org/index.php/Chromium#Hardware_video... for the similarly non-obvious instructions in Chromium (and by the way, currently it's plain impossible in Chrome).
Props to Martin Stransky from RedHat who implemented this for both Wayland and Xorg during the last months.