interesting thread here.
while sampling rate and bit depth are techincally "unrelated", you would want to have a great bit depth when changing sampling rates. you might want to upsample the 44.1 kHz data on CD's to 96 kHz to get the required filters further away from the audible range. an upsampling DAC might do this. now, whether upsampling via a DAC in real-time, or via a software application on your computer, it's just a set of mathematical calculations. the more bits you have, the less audible the "round off" errors will be. think of it as using 24 decimal places instead of 16 decimal places in all the calculations. in fact, when doing signal processing on a computer (including resampling), many software applications use 32 bit or even 64 bits when doing the mathematical calculations, and then drop down to 24 bit at the very end. so that's why you might want to have a higher bit depth when resampling data.
now, to commment on this thought:
Word length is increased by adding noise to the signal (aka, dithering)
actually, dither is usually used when decreasing the bit depth. dither is a very small amount of noise. the idea is to randomize the last bit of data that will be kept. if you have a 24 bit sampling depth, and you just truncate the data to 16 bit (chop off the 8 least significant bits), the result might sound a bit harsh. by adding dither, you essential add a small amount of white noise to the last bit, which the human ear finds more pleasing than digital errors produced by truncation. of course, then you get into a whole other topic of noise-shaping the dither. you can get the results as masking the errors of truncation even if you add noise (dither) that is mostly out of the range of hearing. that's what the Apogee uv22hr or the Sony SBM process is all about (to name just 2 of the many dithering schemes).
but, to answer the original question, if it's just a 24 bit DAC, and it does not upsample the data, then the last 8 bits will just be filled in with zeroes, as Aball mentioned in the first reply.