It you use a 32 bit version of Unix, you might run into problems after January 19, 2038 which is 2,147,483,647 seconds after January 1, 1970.
But if you use 64 bit version of Unix, you don’t have to worry as the date won’t roll over for 292 billion years – 9,223,372,036,854,775,807 seconds after January 1, 1970.
The universe is not expected to last for another 292 billion years, so there is generally not much concerned about that date rolling over.
The best estimate for the universe’s lifespan is about 22 billion years remaining, although there is a 95% chance that human beings will be extinct in 7.8 million years with an 20% chance of human extinction by 2100.