Can an automatic with a transmission going out or slipping or something, lose neutral gear all of a sudden and go into drive?
Anything is possible. Check the fluid level first. If all is good, might be time for a rebuild. BTW: The taurus automatics were not very robust and surprised you haven't had issues till now. If the transmission is indeed ready for replacement, I'd scrap the car, only worth $1K for a clean example.
Search Ford Taurus Questions
Ford Taurus Experts
Related Models For Sale
Used Cars For Sale