Stripers are anadromous. That is they spend their lives in saltwater and return anually to the freshwater rivers that they were born in to spawn.
Anadromous fish can be conditioned to live solely in freshwater. The pure striper requires approximately 37 miles of river with a suitable current for their eggs to remain bouyant, get fertilized and hatch.
(more area is needed in rainy years) Most stocked impoundments dont contain the necessary conditions for natural reproduction. There are exceptions and reproduction has been evidenced in some river chains. One example is the Ace basin in South Carolina and its river chain where these fish have been found to be reproducing naturally. In South Carolina, the rivers that flow south from Columbia provide enough movement for stripers to reproduce naturally.
However most purebred freshwater striped bass fish need to be continually stocked. Without the free flowing current the eggs fall to the floor and suffocate before they can be fertilized and become viable.
The hybrid striper has been stocked in impoundments and in river pools in 30 U.S. states. The thread below outlines the states that dont have stocking programs for hybrid striped bass.
Recently they started stocking again in California. The post doesnt reflect the change as it is somewhat outdated.
Yaz also correctly noted that the hybrids can live in the salt. Record hybrid striped bass has been caught in the Atlantic Ocean as one in the Cape May rips in 1993 weighed in at 12 pounds 7 ounces and one weighing 13 pounds 2 ounces was recorded off of the New Jersey Coast near Brigantine in 2004.