Is this only happening in one direction? One possibility is that the carrier has a different circuit that is provisioned up, HDLC, with no physical connection. A short-circuit in a DACS or MUX is bridging the transmit interface towards your destination with a transmit interface on the unused but active circuit. This would cause your traffic in that direction to fork both on the desired path and some rogue path that eventually gets routed to your destination.

The ethernet equivalent would be a SPAN monitor port plumbed to a transmit-only interface on a different network.

Definitely a strange one. If I'm correct, when the other circuit starts to get customer traffic things will probably break completely for either the new customer seeing your PPP traffic or for both of you.