Safety cases have been used to set out how they will safely deal with unusual or challenging issues for main years. They set out the measures that airlines will put in place to mitigate risks, in this case of flying through ash. They also include input from aircraft and engine manufacturers, which is important as they can advise on the levels of ash that their engines can safely cope with.
A safety case needs to show that the airline understands the hazard and its own limitations, and that it has in place robust procedures and plans to safely fly in the unusual situation. These procedures may include extra training for crews, additional maintenance inspections, and guidance for pilots as to how they shout react in certain circumstances.
Safety cases are put together by the airlines and presented to their regulator (the CAA for the UK) for acceptance.