If only we'd known back then the things we know now.....
My first car had drum brakes and when I changed the shoes I would take a deep breath and blow the dust out of the drums.
Then in the 1980s I worked for a brake and clutch manufacturer at their main factory. Asbestos risk was certainly known about at that time and great care was taken to control dust in the factory. It was a phase where the industry was changing over to non-asbestos products - known as "metallic pads". They're typically made of iron, copper, steel and graphite mixed together and bonded to form the pad material. Our company cars were used as a test bed for products under development, not least because although effective the new materials had a greater tendency to squeal. It was at that time, and related to the factory environment, that I learnt about the use of a Tyndall Beam to see small particles of asbestos dust in the air which would normally be invisible. Essentially like seeing dust indoors in a beam of sunlight or seeing dust in the beam of a cinema projector. Some info on this link
Expert Witnessing and Scientific Testimony
Back in the day people would talk about their brakes being noisy because they were worn "down to the rivets". That's because asbestos linings were fixed mechanically with rivets to the brake shoe/pad or clutch plate. With more modern linings and bonding techniques the rivets are no longer required. This is part of the reason modern cars tend to have some form of brake wear indicator - whether a mechanical squeal device bonded into the pad or an electrical circuit which gets broken when the pad wears past a certain thickness. They are not fool-proof because a jammed caliper can cause very uneven pad wear such that one side of the pad still has plenty of "meat" but the other is "down to the metal". Clearly there will be some nasty noises to alert the driver once the backing plate touches the disc!
Separately, we were starting to make carbon brakes and clutches for F1 cars under the AP Racing brand. They were called carbon-carbon brakes because both disc and pad were made from the same carbon material. It was fascinating because nobody really knew how the material was going to behave in a race car. The carbon material was made by Hitco in USA and had previously been used in aircraft applications where braking events are one off and pretty much standardised. Carbon-carbon brakes were very tricky in race cars because braking was feeble at low temperatures and savagely effective at higher temperatures - so difficult for a driver to know how his brakes were going to react from corner to corner. For this reason carbon-carbon was no good for road cars. Carbon ceramic compounds were developed later and are used on some road cars today.
More stuff about metallic brake pads on this link
How Brake Pads Work