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halfwaytobedlam
I don't think that rubbery substance is brake pad. When pads melt, they smear onto your rotor and form marbling on the metal surface. Pads don't sling off like that; it's not possible (they aren't made of anything that would be rubbery)
If I had to guess, there are a few possible culprits:
- You picked up some rubber marbles from your own wheels, other cars, or the track
- Brake pad grease
- Caliper pin grease