With no paper stock certificates, what guarantees that an investor can get his money if there is catastrophe?

Given that brokerages no longer mail paper stock certificates to investors, how can someone who owns stock be sure they will get their funds out of the market in a calamity (i.e., a computer virus that wipes out all computers/brokerage records)? Although there are insurances for stocks, do the brokerages keep paper records for each client? I have heard of some type of account ("clean....account") that can protect against this risk. What is the answer?

every month print off your brokerage statements and save them. Keep an entire years worth. Also be sure to print off every confirmation of your buys and sells. These are your best defence against having a problem. All disputes with brokerage firms go to arbitration if they can not be mutually reconciled. These are your proof of your side of the case.

It's probably not that safe.

Most online brokers will send you certificates for a price.

If I were you, I'd be sure to keep accurate records on your end. Surely you get a statement (electronically or otherwise) when you first invest or make changes to your portfolio. Keep everything, it may be your only proof in the event of a major disaster.

all the brokers back up their electronic records every night, including to storage locations far away that are protected against even EMP.

there would be obvious delays if an EMP struck NYC -- and the markets would all be closed for an unknown period after which they'd re-open down a lot. And, what remains of your value would still be there.

There are holding agents that are independent of the stock broker that record ownership. You may be mixing two questions, getting paid is different from proving ownership.
I would any dispute regarding ownship is remote. There mulitiple redundant systems that are in different geographic locations and back ups that may be electronic and on tape. And you may have your own records, ie statement and cancelled checks.
Historically there have been major disasters, and back-ups have worked.