In general, the term "folk process" refers to how the music, words may change over the years, decades and centuries. It also refers to the (usual) loss of the author's identity.

Quite often as a song travels from one region to another, people may sing the song, but change it to reflect local conditions, people and times. Also, some words or verses may be forgotten. Other verses can be added, totally new or from other songs.

If you look with search here on an old song such as Barbara Allen. You will find quite a number of different versions. Another such song would be Wild Mountain Thyme. A clear example (can be found in the Forum) is the Nova Scotia Song/Farewell to Nova Scotia. It can be traced back nearly two hundred years to Robert Tannahill's poem/song A Soldier's Adieu. The song in its current incarnation would have been intact by the late 1800s. There were people who remembered it in this form from their youths in some of the collecting by Dr. Helen Creighton.

This still happens. A number of songs which are as recent as 20 or 30 years old are already thought of as "Traditional". Barrett's Privateers and Northwest Passage from Stan Rogers along with Fields of Athenry by Pete St. John are some of these songs. Plenty more of those. They may not hqve the lyrics changed as much as others which are older.

Hope that helps.