Generally it enters the ramp drainage system and flows out with the rest of the runoff. Sometimes its recycled and sometimes its just filtered out of the runoff water and disposed. The EPA has a lengthy report on it you can find here various airports have different methods for recycling it or filtering it out as well as water drainage systems that vary in complexity and scope. The report sheds some light on the various systems involved at different airports.
Longer blurbs are available in the report (see section 7-1) for deeper descriptions.
Ultimately the components of De-Ice fluid break down fairly rapidly when released.
When released into the environment, both ethylene glycol and propylene
glycol are expected to partition to surface or groundwater. They are
expected to rapidly biodegrade and not to persist in the environment.
Biodegradation rates depend on temperature and oxygen conditions and
glycols biodegrade more slowly under anaerobic conditions. The
half-life of ethylene glycol and propylene glycol in water under
aerobic and anaerobic conditions, and in soil are shown below. Note
that these data were not conducted under the same laboratory
conditions and may not be directly comparable (5).
Smaller fields or those that can not afford complex systems may allow it to flow into installed drainage systems right off the ramp. The small field I fly out of has no formal system to dispose of it.