I have a coin that has a Morgan eagle on both sides with no lady. Have you heard of such?
Without seeing your coin, it is impossible to speculate about what you might have. Possibilities include:
(a) An altered two-tailed coin (similar to the two-headed coins) made for novelty purposes or magician's tricks.
(b) Any number of commemorative tokens made through the years, sometimes of good silver but usually base metal , sometimes with a very thin silver plating, which are sold as "collectibles" to unwary people.
(c) A minting error from one of the private mints that make the tokens in (b).
(d) An intentional "error" made by a private mint as curiosity piece.
One thing your coin is not is a genuine U.S. Mint two-tailed struck Morgan dollar. I have more about two-headed and two-tailed coins in my article about two-headed coins, which also explains why such coins are impossible (the die shafts are made differently so the Mint workers can't put a "round peg into a square hole.")
If your coin exactly matches the reverses of genuine Morgan dollars, then there's a decent chance you might have type (a) above. In such a case, the coin might be worth as much as $20 to $25, partly based on the silver bullion it contains, but also because Morgan Dollars altered in this two-tailed fashion are quite scarce.