"Is the re/insurance industry really prepared for a large tail event?"

No.
The plan is to lay any claims over about $50 billion on taxpayers.
That's insured losses not total losses.
Short the re/insurers this year. The probabilities are shifting against them and although it's not a lock it is still the way to bet.

From Artemis:

It’s been questioned whether the insurance and reinsurance sector is ready for a significant tail event that could cause losses of $150 billion or more, or if the industry is too focused on being ready for the next Katrina.

For the first time since 1851 the state of Florida has gone a decade without a landfalling hurricane, and while the insurance and reinsurance industry is prepared for the next Katrina in terms of capital adequacy, events “deep in the tail” are what the industry should pay more attention too, according to Risk Management Solutions (RMS) co-founder and Chief Executive Officer (CEO), Hemant Shah.

“I worry more about our focus on events like Katrina, our tail is very long. When we simulate events, Katrina is not the 100-year loss in the U.S. We simulate events across perils that could cause well in excess of $100 billion in loss, and I think that is the kind of event the industry should be more mindful of, events deep in the tail,” explains Shah.

A consistent inflow of reinsurance capital from both traditional and increasingly alternative sources, as well as the ongoing benign catastrophe loss landscape, has bolstered the market’s overall capitalisation in recent times.

And while the current market sits awash with capacity, resulting in a supply/demand imbalance that continues to pressure rates for both reinsurance and increasingly primary players, it’s expected the sector could absorb a 1-in-100 or 1-in-250 loss event.

Shah, however, feels there “is often too much focus on the 1-in-100 or the 1-in-250” event, and believes the industry needs to look deep into the tail, where “there are some scary events.”

Speaking with A.M. Best, Shah underlined that a $150 billion hurricane along the U.S. East coast, a West coast quake, or a huge earthquake in the New Madrid seismic zone, has the potential to “cause significantly more losses than we’re accustomed to thinking about in the Katrina scale.”...MORE

Total economic losses from Katrina were over $150 billion with around $82 billion of that being property damage. Commercial re/insurance payouts were $41.1 Bil. and National Flood Insurance Program payouts were another $16 billion.

The key to business in the 21st century is to socialize the losses while privatizing the profits.