IIRC the weight given was 8 tons per shot, which adds up to 120 tons for a chain that's 15 shots long.
For us landlubbers, that's a tiny bit more than a fully loaded railroad car. Which will go wherever it wants until it runs into something that weighs a great many times more than itself...like the earth or something, eh. (Got up close when five or six cars of a coal train derailed at about 50MPH.....EXTREMELY impressive, messy, loud and scary.)
Tie down the "bitter end"? Well, yeah but I'd consider that connection to be more a housekeeping touch than anything remotely capable of halting that chain once it got up to speed. JMHO the chain windlass/brake system are really what keeps (or tries to keep) the chain from escaping.
Just stay outta the way if it fails.
Heap bad medicine.
“Tie down the “bitter end”?”
Thanks! I did note that L.P. provided a picture of a Bitt with some line looped on it. (A bight on a bitt?)
I think I saw a you tube of a broken capstan and runaway anchor cable on a Large naval vessel and recall that the seamen scattered pretty quick.
Shown below are Boatswains Mates attaching the pelican hook to the anchor chain of USS Carl Vinson (CVN-70). The pelican hook connects the chain to the chain stopper. They are released with a sledge hammer and doing so can be quite dangerous. 
WWG1WGA
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)
except a shot is a length measurement and each ships chain will have a different weight per shot depending on the required hold for the ship and anticipated anchorage depth.
In the end if it’s running and you see yellow run...if you see red it’s too late to do anything except make peace with your maker.
https://www.youtube.com/results?search_query=anchor+chain+that+gets+away
You’re more right than you know about the housekeeping part of dropping/weighing anchor. First, the windlass does the work of dropping. It’s necessary to throttle the payout or the guides just get too hot, smoke, burn, melt paint. The bitter end is anchored but on modern ships there is a shock coupling that takes the “bang” out of a dead stop.
Reeling the thing back in is the housekeeping part. Nobody wants ground coral, mud, sea growth back aboard, because it stinks, so a fire hose is played on the incoming chain.
But Naval ships don’t drop anchor all that often so they want clean chain back in the locker. A couple of sailors with big paint brushes stand by to touch up the scraped paint on the chain as it comes back aboard. Don’t want rusty chain in the locker either. Except on submarines-—there’s no ready access to the chain locker on a sub.
Someplace around the yard I still have a link of anchor chain I salvaged from a dive I did some decades ago. That link must have 30 coats of paint on it. If a sailor tells you that he worked anchor just give him a hug-—he earned it.