Short answer: yes it is possible.
If, for some reasons, on a PE node there is some kind of misconfigured static route, which are then redistributed into BGP, then we can have a “labeled” loop between two LSR.
But it should not last so long! MPLS TTL will help us and eventually get down to zero!
Sometime it doesn’t.
If on PEs “ mpls ip ttl propagation” is disabled then IP TTL is never decremented while a PE received a “popped” packet.
PE will simply:
Check destination IP address in the label forwarding table
Pick up correspondent label
Do not copy IP TLL to MPLS TTL due to disabled mpls ip ttl propagation
Set instead MPLS TTL to 255
Send labeled packet on the same original interface from where it was received initially.
The same process is then repeated by the PE on the other side of the loop, and still leaving IP TLL untouched.