There wasn’t much room in the title to write the full question, so heregoes:
If I borrowed my Dad’s truck and went out on the road and got in an accident, nobody got hurt, but my license was found to be suspended by John Q. Law, I know I would go to jail, but would my Dad get in trouble for letting me have his truck?
Not if he was smart enough to report it as stolen. 
Generally, though, if you’re the owner of a motor vehicle, you’re likely to bear some responsibility for only allowing it to be operated by persons whom you know, or ought to know, are licensed to operate a motor vehicle.
And you wouldn’t necessarily go to jail. In some jurisdictions, the truck would be impounded, and you would be cited for driving without a valid operator’s license. When your Dad finds out, you might wish you were physically separated from him by some nice strong bars. 
I am uniquely qualified to answer this…IANAL but my stepdaughter loaned my wifes car to a friend or hers with a suspended licence.
SD was the passenger in forementioned vehicle when the friends poor lane change technique resulted in her hitting another car. The friend also fled the scene despite dozens of witnesses who hung around to make statements.
Final verdict, cost me $4,100 to fix the other guys car. Car was also impounded , another $500, and was no longer drivable. Insurance would not touch it because they could draw a chain of permission to an unlicenced driver this is part of why you don’t let your kids file police reports unsupervised. We were not cited but both of the girls were.
Our only option is to try and sue a 22 year old single mom college student (the friend) and thats a mighty dry turnip under the best of circumstances.
My 8 year olds are so never getting cars when they get old enough…
Did you borrow it, or did you “borrow” it?
I was on the receiving end of a similar situation. I was rear-ended; the driver of the car told me she was driving her cousin’s car, but the car was registered only to the cousin’s husband. His insurance company called me later to say they were not covering it because she didn’t have permission (although she was apparently legally licensed). But my insurance company covered it under uninsured motorist coverage. I can’t imagine why you were held responsible for the other guy’s car–wouldn’t his own insurance cover it?
Doesn’t the SD’s friend face some sort of serious charges for driving on a suspended license?
As to the OP, did you have permission?
Two things here. Laws vary greatly from state to state. YMMV. Yadda yadda yadda. I can only speak from a New Jersey law enforcement point of view. For one thing around here you don’t get arrested for driving while suspended. It is a serious traffic violation but you get a ticket and a court date, just like a speeding ticket. I know that is different in other states. As to your main question, we have a statute that covers it. 39:3-40h says it is illegal to permit a suspended driver to operate a motor vehicle. It is a subsection of the suspended driver statute (39:3-40) and it has some hefty penalties. It is also very difficult to prove. Not only would your father have to let you borrow the car, it must be proven that he knew you were suspended. I’m sure many other states have similar statutes.
Oh they did…guess who we wrote the check to…
As Loach mentioned they cited SD’d friend for driving on suspended licence and the at fault accident. SD was cited, not sure what for, (long story, we didn’t see her for a few days after that.)
Assuming you get a favorable judgement, wouldn’t that be good for a number of years and renewable? Personally, I’d go after her but be lenient on the timeframe for collection.
Already discussed it with a lawyer, not worth the legal fees, and SD has thus far been very uncooperative with regard to locating her.
Trust me, if this girl hits the lottery, we will find her OD’d in an alley 3 days later or something equally brilliant. If she makes anything useful of her life in the next 10 years, I’ll eat my hard drive.