Ensure that the faucet and shower head do not leak while not in use. You can take every step possible to prevent shower leaks, but if the faucet itself leaks, water can penetrate the surrounding areas even while not in use.
Install a shower pan inside the shower. A shower pan is angled downward so that water pours to the center drain of the shower, rather than pouring out the edges. Handicap-accessible shower pans do not have edges, allowing them to be wheelchair-accessible. Some shower pans can simply be placed inside the shower stall and sit loosely on the tile, while others must be screwed in. Consult your shower pan's installation manual for more details.
Roll up a towel and place it along the edge of the shower. While a towel does not offer a permanent solution, it is a quick way to stop showers from leaking during brief use.
Install a weighted shower curtain in the handicap-accessible shower stall. A weighted shower curtain is extra long and has internal weights along the bottom of the curtain. These weights keep the curtain firmly in place and prevent water from escaping while the shower is in use.