Before Jenna's mom dies, she gives her daughter and Mia each a friendship bracelet and makes them promise not to take it off. In this moment, we can see Jenna's mom trying to make sure her daughter always has Mia by her side, making sure there's someone she can go through life with once she's gone.
And indeed, this is what happens. Jenna and Mia are best friends of the truest sort, spending all their time together and supporting each other through thick and thin. Fast-forward a couple years, and these friendship bracelets are full of grime, representing both the steadfastness of their friendship and the fact that they've been through some messy and hard stuff together. This is why it's such a big deal when Mia's bracelet rips:
As I open the back door, my friendship bracelet gets caught on the latch and a thread rips. Sucking in my breath, I tuck the broken ends back in place so Jenna won't notice. Maybe we're getting too old to wear them after all. (9.101)
Two interesting things happen here. First, we see Mia panic a big—she "suck[s] in" her "breath," making it clear that this moment registers for her as at least slightly alarming. But then she hides the tear from Jenna and considers the possibility that they're "getting too old to wear" these bracelets any longer. The tear, then, isn't in the bracelet half so much as it's in their friendship. As Mia's been swept up in the world of synesthetes, she's let Jenna fall to the wayside, so when she considers not wearing the bracelet anymore, we know she's really considering not being so close to Jenna anymore.
Say it ain't so, right? Fear not. Before long they get new and improved bracelets—this time made of metal instead of thread—making it clear that this friendship is going to stick around for a long time. If anything, Mia and Jenna are stronger than ever. Phew.