If the ferrite is intact physically, and you can remove the broken wire and some of the glue (pretty easy usually). Then you install a new piece of wire of the same gauge, remount the part and it will work fine.
If you can’t reuse the actual ferrite bead things get tricky.
Determining the actual specifications for a random ferrite would likely cost a few thousand dollars in EMI lab fees. So if the manufacturer won’t provide details, some very tough choices have to be made.
The first is legal liability which is all over the place depending on where you live. For the rest of this post I’m assuming the USA, therefore FCC rules and regulations. Other parts of the world have far stricter regulations so in some countries you can’t proceed any further.
Often these parts are used only because without it the device exceeds the legally allowed radio emissions in some band between DC and daylight.
So if you’re a professional doing this for somebody else, you should give up. This is because you don’t want the FCC knocking on your customer’s door and telling them they can’t use the device you repaired because it’s illegal to use.
If this is a personal device you can take advantage of what I think of as the hobbyist exemption in FCC rules. As a hobbyist there is no fine for accidentally interfering with radio communications as long as you stop doing it the moment the FCC notifies you to stop. So you can experiment cheaply and you’d have a good chance of finding a workable replacement.
The basic steps would be to operate the device with just a jumper wire. Determine if there is any noise in the sound output when the ferrite is missing. If there is noise, you’ll need to try some similar sized beads to find one that removes the noise from the output.
If there is no noise on the sound output, you need to see if you can detect any interference to other devices. If you find the device is interfering you then try different bead formulations of about the same size until the interference is no longer a problem.
If you don’t have detectable noise on the output or at radios receivers, you just choose one that is about the same size and don’t worry about.
Then you just remember that if the FCC comes calling, you cooperate fully, turn off the device and never turn it on again.