There is no specific %. The more accurately you want to understand the amplifier, the more details you need to fill in.
Exact maximum voltage swing you get out of amplifier depends on the engineering details. For example, very low-resistance MOSFETs can go just millivolts away from the rails, and assuming the rails are produced with regulated supply (say switch mode, for example) to a stable value, you get practically +/- 20V swing from +/-20V rails.
On the other hand, if the rails are non-regulated and have the rectified mains ripple (100Hz or 120Hz) riding on the top, say, the rails ride between 18V and 20V at full load, then if you try to go any further than +/-18V, you periodically run out of voltage, but at other times get higher; meaning, the mains ripple goes through to the speakers. So you need to limit the swing to the lowest voltage available to avoid this.
Or, a certain power stage might use Darlington transistors with large saturation voltage drop, say over 1V. Then your 20V supply with 2V ripple only gets you up to 17V.
Maybe the final stage is a voltage follower (voltage gain = 1), and even if the transistors could get closer to the rails, the previous stage cannot.
This is just the tip of the iceberg. It's always case-by-case and requires understanding of the actual circuit used.