This can be a complex problem and response to insulation failure should be considered in the emergency response guidelines and procedures. 
First, a tank with an insulation failure may boil off at an elevated rate which applicable codes build into the relief device and vent system design.
Second, ice and oxygen enriched liquefied air can form where inadequately insulated surfaces are exposed to air. Ice is the most likely symptom of insulation failure, and this can lead to various issues such as higher probability of seal leaks, additional weight loads on piping, and frost heaving of the foundation. Loss of vacuum insulation rarely leads to creation of liquified air, but as a precaution, any material that could be exposed to liquid air must be compatible for both oxygen and cryogenic hazards. For example, flammable materials such as asphalt are not permitted below LH2 systems.