Do companies recover carbon dioxide and water from the purification step of cryogenic air separation, and how?
It is unlikely that this is an economically feasible $\ce{CO2}$ recovery method, which means commercial gas producers probably don't bother to isolate $\ce{CO2}$ this way (surely not water). The removal of $\ce{CO2}$ and water is performed with a pre-purification unit (PPU) that contains an adsorbing material such as alumina or molecular sieve. When the material nears saturation with impurities, the PPU needs to be taken off-line for regeneration. This is done by flowing warm $\ce{N2}$ over the adsorbent to heat it. It certainly seems possible to attempt capture of the $\ce{CO2}$ at this stage. Water is likely to be released from the adsorbent after the $\ce{CO2}$, allowing in principle a stream containing CO2 and N2 to be isolated. However isolation of $\ce{CO2}$ from this stream is expensive. As explained in a brochure from the CO2 Capture Project:


$\ce{CO2}$ can be separated from other gases by cooling and condensation. Cryogenic separation is widely used commercially for streams that already have high  $\ce{CO2}$ concentrations (typically &gt;90%) but it is not used for more dilute  $\ce{CO2}$ streams.
A major disadvantage of cryogenic separation of  $\ce{CO2}$ is the amount of energy required to provide the refrigeration  necessary  for  the  process,  particularly  for  dilute  gas  streams. Another  disadvantage  is that some components, such as water, have to be removed before the gas stream is cooled, to avoid blockages.
Cryogenic separation has the advantage that it enables direct production of liquid  $\ce{CO2}$, which is needed for certain transport options, such as transport by ship. Cryogenics would normally only be applied to high concentration, high pressure gases, such as in pre-combustion capture processes or oxygen fired combustion.


This is complemented by information provided by Universal Industrial Gases Inc.:

Producing carbon dioxide as a commercial product requires that it be recovered and purified from a relatively high-volume, CO2-rich gas stream, generally a stream which is created as an unavoidable byproduct of a large-scale chemical production process or some form of biological process.
In almost all cases, carbon dioxide which is captured and purified for commercial applications would be vented to the atmosphere at the production point if it was not recovered for transport and beneficial use at other locations.
The most common operations from which commercially-produced carbon dioxide is recovered are industrial plants which produce hydrogen or ammonia from natural gas, coal, or other hydrocarbon feedstock, and large-volume fermentation operations in which plant products are made into ethanol for human consumption, automotive fuel, or industrial use.  Breweries producing beer from various grain products are a traditional source.  Corn-to-ethanol plants have been the most rapidly growing source of feed gas for CO2 recovery. CO2-rich natural gas reservoirs found in underground formations found primarily in the western United States and in Canada are another source of recoverable carbon dioxide.