MPLS BFDis configured, and there is an LSP that's UP, for which there exists a BFD session. From the LSP ingress router, BFD packets take the same path as that of LSP. For BFD packets sent by LSP egress to ingress for the same session, the path could be different. LSP egress router uses the shortest path as found by the IGP which may be different than the path traversed by the LSP. In such a scenario, any link breaks in the IGP shortest path from LSP egress to ingress will cause the BFD session to go down (as LSP ingress stops to receive BFD packets until IGP converges). The BFD session going down will bring the LSP down.
MPLS BFDwas intended to detect any failure on the LSP path, but when the BFD's return path is different than the LSP's, any fault on the return path will cause the LSP to unnecessarily go down.