The rear derailleur is often bolted to a part of the frame called a derailleur hanger. Sometimes the bike falls over or gets bashed and the derailleur hanger breaks, which can ruin the frame. Hence, the invention of the replaceable derailleur hanger.
But if you cannot get a replacement, it is not really replaceable.
The basic idea: make the replaceable hanger weaker than the frame. If something gets basho'd, the replaceable part is a "fuse" and is the thing which breaks. Unscrew the broken one, screw on a good one, and off you go.
From http://bikehugger.com/images/12810055073_f54f5356ea_o2.jpg via http://www.bikehugger.com/posts/replaceable-derailleur-hanger as of 2017/12/09; and from https://c1.staticflickr.com/3/2469/4150654217_a19cf912ec_b.jpg via https://www.flickr.com/photos/huggerindustries/4150654217 as of 2017/12/09.
Bad idea: replaceable derailleur hangers. No, not the basic idea, but rather the incredible range of incompatible designs.
The basic idea is simple: your derailleur occasionally gets whacked, and it acts like a long lever arm on the frame, so whacking the derailleur can bend or break the frame. So instead, make a hanger which strong enough for normal use, but in the event of a derailleur whack, the replaceable hanger acts as a "fuse" -- it breaks, saving the frame.
But "the devil is in the details"...
The first practical problem with this idea is that there is no particular standardization. There are, for sure, more-common and less-common designs, but no clear "everybody uses A or B."
According to one site, there are over 450 different models. This seems crazy: I can understand that when there were three models, a bike designer might look and say they want something radically different. But: once there were 397 models, what was it that somebody needed that was so different from all the exsiting 397 models, that there was any real advantage to introducing model #398?
This is a practical problem for you the bicycle rider, because no bike store can afford to stock all the different models. Or even a small fraction of all the models. So when yours breaks and you go to your local shop, the odds are about 450-to-1 against you that they will have the 1 you need. Okay, the odds are probably not quite that bad, but the odds are against you: if you arrive with a broken bike, you will likely leave with a broken bike.
You can work around this to a degree by getting a spare and carry it in your tool kit. Each time you break one, ask your shop to order another. It is certainly possible you will break a hanger two days running, but very unlikely.
A second practical problem with replaceable derailleur hangers is that at least some of the designs weaken the frame. The right rear dropout already leads a hard life. Even relatively-tough old-fangled steel frames with built-in hangers are somewhat prone to break the right rear dropout.
Some replaceable hanger designs remove material from the hanger, drill holes, or do other problematic things to the shape of the dropout. These can weaken the dropout, so if you just go ride a bunch, and even if you never whack the derailleur, you may still break the frame — specifically, the right rear dropout.
But: since there are no particular standards here, it is hard to know from experience which ones are more-durable and which ones are less-durable.
And this one is a bit harder to work around -- a frame break is less likely, but they do happen, and it is not likely you will be carrying a spare frame.
So that said, I like replaceable derailleur hangers.
About maybe 10 of them. The other 440 should just go away.
In 2019, SRAM introduced the "UDH" or "Universal Derailleur Hanger". Designed to solve the mess above, it is available for anybody to manufacture royalty-free, has a suggested retail price of US$15,and will mount derailleurs from all brands (not just SRAM).
From https://www.vitalmtb.com/photos/features/PIT-BITS-2019-Crankworx-Whistler-Bikes-and-Tech,12546/Universal-Derailleur-Hanger-on-the-2020-Trek-Fuel-EX,131882/sspomer,2 as of 2019/09
This is a good direction, but it is not yet smooth sailing:
It is not yet clear that the design is a good design. Anybody can declare something a standard. But if the design has problems, you don't want to use it. Time and testing should tell if the UDH works well.
A quick check as of 2019/09 shows shops selling it for slightly more than the suggested retail price. This is only a minor issue, since over time, low-cost versions should be available widely.
At least some write-ups suggest it fits only "mountain" bikes, though without explaining why. One says [link as of 2019/09]:
[W]e’d happily put money on manufacturers putting pressure on SRAM to make it or a slightly modified version available for road bikes too.
A slighlty-modified — and incompatible? — universal hanger.
One version for road and one for MTB would be better than today's 450 versions. But it is easy enough to imagine the number will grow to more than two over time.