I first thought they used a vacuum of air so they don't dislodge the components after they've placed them?
Electrical – How do pick and place machines pick up components
pcb
Related Solutions
Autosplice (and possibly others) make solderless teminals like these:
See the datasheet here. These can be pressed into the PCB with some gentle force if you don't have too many pins to connect at one time. You'll need to solder the straight end into the main PCB.
Note that neither these headers nor the PCBs you press them into will have high cycle counts - The headers will flatten, and the hole plating on the daughter cards will be gouged by the headers. Note also that the connection won't be as durable as a soldered link; don't subject these to lots of vibration or tension from a cable connection. If either of these problems are a showstopper, you'll need a standard connector with a soldered link.
However, for your "In case they fail" application, this should be a fine solution. Sparkfun is out of stock, you can email the manufacturer at sales@autosplice.com or look at their distributors.
The machine will detect failure to pick a part up to the point where the vision system sees it, but not usually afterwards. The normal process is for PCBs to be visually inspected, either manually or automatically as a seperate process after placement, to detect misplaced or dropped parts. Most P&Ps will probably not know they have dropped a part after it has been imaged, although it is possible some might sense placement pressure and/or vacuum pressure to detect drops, however if set up properly, drops shouldn't really happen.
Best Answer
Using a vacuum pickup. Those are handheld ones, but the machine has one on a robot arm with XYZ control.
It's very simple, just a tiny suction cup with a vacuum that can be turned on and off.
The components are placed onto the solder paste which is slightly sticky, so small vibration won't dislodge them. If the board will be double-sided, a small dot of glue is added before the component is placed. This prevents the components falling off when the other side is being soldered.
Then the board goes through the oven, is subject to optical inspection to check that the parts have soldered correctly, and any parts that can't be handled by the pick and place machine are hand-fitted and hand or wave soldered. This is usually only required for big connectors.