Hello,
I have a 2004 Ford Taurus but I did some work on it a few months ago and it required taking this part off and it keeps slipping off now.
I’m curious what part this is and how I can stop it from slipping off. I know it is part of the throttle but is there a way to keep it on. It just slips over another plastic pace and eventually works its way back off. That results in the car accelerating on it’s own.
Picture attached
There is a clip that fits into the groove you see. The clip goes on after the throttle shaft is placed on the pin. It had to have had one before you started “working” on it. They don’t just dissolve so you had to have removed it somehow. They tend to 'pop" off at speeds high enough to bend space and time. That’s why you can never find them again… they end up in a parallel universe! 
Looks something like this… the parts store or even a hardware store should be able to help you out.
I have a 01 Taurus. It has no clip. To detach you slide it parrallel from linkage towards back of engine to take it off. To put it back you slide it over the nub towards the front of the engine until it snaps in. Repeated removal could wear out the plastic end or pulling it out sideways can damage the plastic end. I’m not sure but the end may be replacable. If not, the cable needs replaced.
Not familiar with that exact setup but the end looks like it is supposed to have interference fit to snap over the pin with the slot. It could be damaged from prying it off. Hard to tell as picture is out of focus.
Another issue is how the engine can accelerate on its own if the cable comes off. There’s a big return spring(s) meant to ensure that the throttle returns to idle if you let off the gas pedal or this cable comes loose. You should look closer to see if all the springs are in place and ensure nothing is interfering with the throttle movement…
