Short answer:

"Bucket shops"

Discussion:

The man on the street often bought shares in storefronts that essentially sold you a bet on the price of a company, without actually delivering a share. These early derivative bets were legal until early in the 20th century.

Back in the day, purchasing a share was a mechanically complex and expensive procedure, requiring a banking relationship and physical delivery of share certificates -- stock "portfolios" once were actual physical portfolios, holding pieces of paper. Stock certificates, Bonds with attached coupons - little strips of paper which the bondholder physically cut and presented to the payor for interest payment. Not too many people actually directly owned shares-- one estimate is at just before WW I the total was perhaps 500,000.

That was all difficult for wannabe small investors, who would hear of stocks going up and might want to get in on the action, but might lack the relationships to purchase shares. He might also lack the funds to purchase a full share as well -- if you have five dollars and the share price is $40, it can't be bought on the exchange.

So he went to an entrepreneur with a storefront a stock ticker -- the enabling technology-- and placed his bet on share price, rather than actually owning a share

The term "bucket shop" apparently originated in early nineteenth-century England. Poor youths drained beer kegs thrown out by pubs and sold the collected dregs in abandoned shops. In the late 1870s the term was applied to shops where customers could wager on the price movements of stocks and commodities. Bucket shops leased tickers from telegraph companies on the same terms as brokers did and used real-time quotations from exchange floors as the basis for customers' wagers. However, bucket shops did not place customers' transactions on any of the stock and commodity exchanges, nor did bucket shop transactions affect the actual prices of stock shares or agricultural products. Such transactions were fictitious and did not result in delivery of stock certificates or commodities to their patrons

The interplay of the bucket shop and the listed security gave rise to all sorts of scams-- but it's interesting to think about just what the bets that the bucket shop sold actually were. They were effectively an unregulated off exchange derivative product, backed only by the operator's credit and reputation. Your bucket shop bet might be placed on a company whose equity soared, but you might be out of luck. Compare with placing a bet with a bookie-- you can get the spread right, but if your bookmaker can't pay, there's not much recourse. If you bet on the Packers and win, you can't go to Green Bay to collect your winnings . . . if you bet on the the Great Northern, James Hill wasn't going to cut a check if the bucket shop failed.

So how would you do this without being fleeced? That would be a hard problem-- you could be. Particularly for a would be long term investor, exposure to the bucket shop's promise would be a substantial risk; to the extent that they could be relied on at all, the shorter the holding period the better. Jesse Livermore -- a celebrated speculator -- described how he saw the risk

Anyhow, at fifteen I was making a good living out of the stock market. I began in the smaller bucket shops, where the man who traded in twenty shares at a clip was suspected of being John W. Gates in disguise or J. P. Morgan traveling incognito. Bucket shops in those days seldom lay down on their customers. They didn’t have to. There were other ways of parting customers from their money, even when they guessed right. The business was tremendously profitable. When it was conducted legitimately—I mean straight, as far as the bucket shop went—the fluctuations took care of the shoestrings. It doesn’t take much of a reaction to wipe out a margin of only three quarters of a point. Also, no welsher could ever get back in the game. Wouldn’t have any trade.

He wasn't concerned with the bucket shop as custodian for a long term investment; his bet would resolve in a day or two, weeks not months, months not years.

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Sources:

Hochfelder, David. “‘Where the Common People Could Speculate’: The Ticker, Bucket Shops, and the Origins of Popular Participation in Financial Markets, 1880-1920.” The Journal of American History, vol. 93, no. 2, 2006, pp. 335–358.

Cedric B. Cowing, Populists, Plungers, and Progressives: A Social History of Stock and Commodity Speculation, 1890-1936 (Princeton, 1965)

Ann Fabian, Card Sharps and Bucket Shops: Gambling in Nineteenth- Century America (New York, 1999)

and for a flavor of the times, see the classic

"Reminiscences of a Stock Operator" -- written under the name "Edwin Lefevre", but generally thought to be the autobiography of the celebrated Jesse Livermore, who played all sorts of games with the bucket shops n the last decades of the 19th century. A good description of the mechanics and the rough and tumble caveat emptor spirit of the times.