[edit: here's the episode, very interesting listen: http://www.thisamericanlife.org/radio-archives/episode/377/S...]
One of those happened just last week:
http://www.fdic.gov/bank/individual/failed/commbank-ct.html
So it seems like in an instance like this, while you get a check for your insured deposits from the FDIC, your bank is gone and presumably any auto-debits or outstanding checks would fail to clear. You get to wait for the FDIC to mail you a check. Then you'd have to find yourself a new bank. This seems like something that would be fairly disruptive even if you are not poor.
Also, if you chose to forgo paper statements to "save the environment" (and reduce the bank's costs), and you were lax in downloading your statements, it would probably take even longer to be reimbursed.
No bank statements or formal claim for reimbursement is needed; the process is entirely automatic and usually done in less than 24 hours.
In most cases, the FDIC takes over the bank and runs it (in a matter of hours), specifically to prevent this sort of impact.
Within the last century, yes, but quite far back within it: the last time anyone with modest amounts of money in the U.S. lost deposits in a bank failure was 1933, the year the FDIC was created.
You can still lose money in a bank failure if your deposits are above the FDIC insurance limits, but poor people by definition would not have that much money, so it wouldn't explain their choice not to use banks.