What I'm referring to are Safe Haven Laws—protection for mothers who are unable or unwilling to care for their newborn babies. How do Texas Safe Haven Laws Work? The Safe Haven Law, or the Baby Moses Law, was first introduced in 1999 under the Texas Family Code. The child must also be unharmed in order for the Safe Haven site to take over and begin the adoption process, free of charge. Baby Boxes in TexasSome fire stations in Texas have specialized containers called baby boxes that are designed for secure and temporary holding for newborns.