If the Kaplan-Meier survival curves cross then this is clear departure from proportional hazards, and the log rank test should not be used. This can happen, for example, in a two drug trial for cancer, if one drug is very toxic initially but produces more long term cures.

Can Kaplan-Meier curves cross?

Please keep in mind that the Kaplan Meier curves can cross each other when there is no difference between treatment/exposure groups.

Can survival curves cross?

Crossing survival curves is generally a result of the survival times having greater variance in one treatment group than another.