The year 2038 problem is a Y2K bug of the programming world. On January 19th of 2038, the 32 bit unix timestamp will be unable to count forward any further and will instead interpret future time to take place starting in 1901 (I guess time travel will be discovered in 2038 for many devices). 
As reported with the Nexus 7 devices, the Google pixel has a similar way of postponing issues brought about with this bug – prevent that time from ever existing.
So what happens at 11:59 PM December 31st of 2037? Time continues on. A minute later my phone displayed January 1, 2038. Unfortunately, I’m not going to keep my phone’s datetime settings out of whack for 3 weeks to find out what happens. Considering the Pixel runs on 64 bit architecture, likely the only issues would be with apps still using 32 bit unix time.