I just came across two journal articles that match my understanding of what became of many of the Lenape (Lenopi) in South Jersey. They are still here!
"After the sales of their lands in the 1600s, most Lenopi simply withdrew to areas in their collective territory, such as swamps, that were less attractive or useful to colonial immigrants....most Lenopi never left their homeland" (Becker, 2010: 63).
"Many [Lenopi] intermarried with the colonists during the earliest period of contact" (Becker, 2010: 68).
"Many, if not most, of the descendants of those Lenopi. who loved elsewhere in New Jersey when the Brotherton tract was occupied (1758–1802), never left the area. Their stories remain poorly known" (Becker, 2011a: 74).
Becker makes a good argument that South Jersey's native population ("Jersey" or "Lenopi") was distinctive from their brethren across the river ("Delaware" or "Lenape"). It is a controversial viewpoint. Read the papers and decide for yourself.
S-M
Becker, M.J., 2010: The Armewamus band of New Jersey: other clues to the differences between the Lenopi and Lenape. 80, 2: 61–72.
Becker, M.J., 2011a: Jacob Skickett, Lenopi elder: preliminary notes from before 1750 to after 1802. 81, 2: 65–76.
Becker, M.., 2011b: Lenape culture history: the transition of 1660 and its implications for the archaeology of the final phase of the Late
Woodland Period. Journal of Middle Atlantic Archaeology. 27: 53–72.