This article proposes a global escape mechanism which can handle unexpected or unwanted conditions changing the default execution of distributed communicational flows, preserving compatibility of the multiparty conversations. Our escape is realised by a collection of asynchronous local exceptions which can be thrown at any stage of the communication and to any subsets of participants in a multiparty session. This flexibility enables to model complex exceptions such as criss-crossing global interactions and error handling for distributed cooperating threads. Guided by multiparty session types, our semantics is proven to provide a termination algorithm for global escapes. Our type system guarantees further safety and liveness properties, such as progress within the session and atomicity of escapes with respect to the subset of involved participants.