During the transaction through LN, the information is transmitted sequentially. Any participant of the transaction can transfer information only to the previous one or to the next one. This means that all participants cannot simultaneously come to a single decision regarding the transaction status.
For example, let's take the status of a transaction - that it is completed and cannot be canceled. and we have a chain of nodes
A<->M1 <-> M2 <-> ... Mk ... <-> Mn <-> B.
Let node A decide that the transaction is final and passes information about it to node M1. M1 passes M2, etc. the information reaches node B. What happens if the Mk node fails at the time of transmitting this information. Nodes A, M1, ..., Mk-1 will assume that the transaction is completed. And the nodes Mk+1,...Mn,B will remain in uncertainty.

These are theoretical reflections. I don't see a solution to this problem. Therefore, it is interesting to know how this problem is solved in LN.