“Chain of custody” essentially means an authorized person could vouch for its whereabouts at all times. So, let’s say I’m the vet doing drug sampling. I draw the blood. I label it. I record it and I sign/initial somewhere on that record. It goes into my pack until I pass it on to the next authorized person. They examine it, agree that it is labeled and appears as expected, and they sign off on it. In most cases that middle man isn’t the tester, they’re a transporter or the front desk. So they get it to the person testing it, who also takes a look at it, makes sure the labels and appearance match what’s expected and they sign off on it. Everyone along the chain is expected to verify what they have and sign off that no unauthorized person handled it and the labels match the expected sample every step of the way. Each name who signs of on it is a link in the chain of custody, so that you can’t say “well, we don’t know how it got from A to B, which means my rival, Cheaterton, may have gotten his hands on it and made a switcheroo!”
The chain is broken if: it gets handled by an outside party (someone who might adulterate the sample or switch it for a clean/dirty one), it goes missing in someone’s care, the label doesn’t match (names are important - if I say my sample is from Medina Spirit, but I label the tube with his barn name, we could have a problem.) Honestly? The most common break in the chain of custody is something silly, like somebody puts it in a freezer and it gets lost or goes missing. At this level, I’m sure the baggies for transport are sealed and are only broken by authorized individuals, so you’re going to pretty quickly find evidence that somebody popped your baggy open and broke the chain of custody.