Meaning of TLC59281 LED supply voltage rating
17V really is the maximum voltage which can be used to supply the LEDs with this IC.
When an output is turned off, then the LED supply voltage is applied to that output pin (since no current flow means no voltage drop across the LEDs).

This IC isn't intended to drive long strings (at least not without a little extra voodoo on its outputs) - its not a 'string driver'.