A bank has assets, the money you lent the bank (through your deposit) is invested in a mortgage, backed by a property. You will ultimately get your money back. but it is a timing issue (and therefore liquidity), not a solvency issue.
Madoff just paid a dividend or phony appreciation to investors based on money deposited by new investors -- except for the money he stole it was a closed system with no return generated.
He also concentrated his efforts on courting a relatively insular community (religious Jews) via trusted community figures to avoid awkward questions.
Thats usually a sign of a scam -- banks don't send your priest/rabbi/community leader to hawk CDs. But there are many hustles (Ponzi schemes, pyramid schemes, and various savings clubs) that are common in ethnic and religious communitiesand apread via word of mouth.