Something fell off?

That's the important part of a disc brake pad. Is there a chance you simply hit it on the road and it came from a different car? These linings have been known to rust off their metal backing plates, but as soon as that happens, you would observe the brake pedal goes further to the floor the next two or three times you press it. With enough pedal strokes, that brake will self-adjust, then the brake pedal will feel normal again, however, the metal backing plate will be grinding on that brake rotor. You will hear that. The grinding is going to wear that rotor down very quickly. That can lead to total loss of front or rear brakes, and in some cases can cause that wheel to lock up.

If a mechanic looks at this right away, the cost is likely to be little more than that for a normal brake job. At the mileage you listed, it's getting close to time for a brake job anyway. Also, to keep weight down, brake rotors are made so thin that they often can't be machined, like we always did in the past, and remain above the published, legal limit. Today regular, or normal brake jobs usually have to include new rotors too.

In this case, the tabs on each end indicate this IS that metal backing plate. I've never seen that part fall off as those tabs keep them in place. If I found this on the road, my first thought would be it fell off someone's load of scrap metal on the way to the recycler. Do you hear any unusual noise when braking? Any warning lights on the dash? How do the brakes feel?

On a CTS-V that could be a rear brake pad backing plate that holds the material that stops the car. Normally they should look like the image below. I have seen brakes fail this way, the tabs that Doc referenced normally hold the pads in place, however on the calipers in that car it is possible that a bare plate like that can fall out if the other pad is also worn, it allows enough room that the backing plate could slip through the opening between the caliper and rotor.
The problem is then, if it's the outer pad that failed, the caliper will be scrubbing the rotor, If it's the inner pad the brake caliper pistons will now be scrubbing the rotor. If this just fell out I would have the car towed to the shop and have all the brakes checked. If the pistons haven't started hitting yet, a simple brake job with pads and rotors, probably on all four corners if that wear is any indication of the others. If they have started hitting then you will need at least that caliper.

It's time for a brake system check. Any independent shop or the dealer can do that for you. For this type of work, the dealer can be no more expensive than any other shop, but if you compare repair estimates, be sure you're getting the same things at each shop. For example, machining the rotors that I mentioned. There is a legal thickness that no reputable mechanic will go beyond. Years ago it was common to machine rotors two or three times, once at each brake job, when they were really fat to begin with. In the 1970s to 1990s, new rotors could cost up to $100.00 each. Part of the cost of the brake job included the "consumables", meaning the cutting tools and machinery used to perform the job.

Today most rotors are very thin and have already worn beyond their usable thickness by the time a brake job is needed. Replacing them eliminates the cost of those consumables, and the mechanic's time to do the machine work. The good news is rotors for newer models can be as low as $20.00 each. It's a better value for you to just replace the rotors as part of the brake job.

The mechanic can give you an estimate of the percentage of brake linings that were left on the other brake pads. We never go by mileage because there's way too many variables in how people drive. "Percentage remaining" is a better indication of the life left in the pads.

There are grooves, or notches, in the mounts the pads sit on that we slide those tabs into, then, once the caliper is installed, those pads are held captive, or in place. As the linings wear over many miles, those tabs gradually slide along the notches to stay in constant adjustment. The only way to get the pads to slide far enough to pop out of the notches is to remove the caliper, ... Or for the lining to rust off, giving the remaining metal backing plate extra room to slip out. Most designs don't offer enough room for a pad to fall out without removing the caliper, but on some models, it is possible.

The bottom line is you need a standard, or typical brake job. This isn't anything we haven't run across before.