lol. Funny you use the term, "Handshake". That's the term used when computers connect.
Not to worry:
For example, TDAmeritrade alone has ~10,000 employees. Records and transactions have multiple data locations and storage; data redundancy; your personal electronic records; MM Transactions; Brokers' filings, monthly and yearly; IRS reports by the Brokerage, SEC, FINRA...yada, yada, yada. Losing your shares is no more plausible than the world being hit by a virus pandemic. What could possibly go wrong? ;-).