Can a serpentine belt loosen over time?

Can, but today's belt construction and materials the stretch is minimum. There are self-adjusting belt tensioner on most cars today that the would take up the slack also.

Edited: Very old method of inspection is if there are cracks in the ribbing of the belt. It does not apply to newer belts. Just replace them at around every 100,000 miles.

Your question is good, yes the belt like any rubber will expand with time. Just like the other people here say the tensioners job is to adjust the belt as this happens. Now have after a period of time the belt can pop, or shows signs of extreme wear. At this point it is recommended to replace the belt. If you then realize it comes off again or its loose for some reason, you should check if the tensioners are working properly.

Most new cars come with EPDM belts. They last much longer than Nitrile. The auto tensioner takes up any slack until it wears out. Then you'll have squealing problems. See the post below

Any belt will stretch over time but the belt tensioner takes care of this for you.

the source of tension can wear or get weak so there is a chance. the serpentine belts should not stretch.