If I borrowed a friend’s car that was uninsured and had an accident, can the other driver go after my friend or his assets or is it fully my responsibility?

If you were at fault in the accident, the registered owner of the car you were driving is liable for the property damage to the other driver's vehicle and the personal injury claims of the driver and any other occupants of that vehicle.  If the other driver had uninsured motorist coverage, the other driver could file a claim through their insurance company, but their insurance company will sue your friend (the registered owner of the vehicle you were driving) for the amount paid on the uninsured motorist claim.  If the other driver did not have uninsured motorist coverage, that driver will sue your friend, the registered owner of the vehicle you were driving, for negligence.  Your friend could sue you to recover the amount of the judgment against him.  You will also be named as a defendant in the lawsuit for negligence filed by the other driver.

If you were not at fault in the accident and the other driver had insurance, a property damage claim for the vehicle you were driving could be filed by your friend, the registered owner, against the at-fault driver's insurance carrier.  If you were injured in the accident and were not at fault in the accident, your personal injury claim would be filed with the at-fault driver's insurance company when you complete your medical treatment and are released by the doctor or are declared to be permanent and stationary by the doctor which means reaching a point in your medical treatment where no further improvement is anticipated.  The personal injury claim should include the medical bills, medical reports and documentation of any wage loss.  Compensation for the medical bills is straight reimbursement.  Compensation for wage loss is straight reimbursement.  The medical reports will document the nature and extent of the injury and will be used to determine compensation for pain and suffering, an amount in addition to the medical bills.  If the case is NOT settled with the insurance carrier, a lawsuit for negligence against the at-fault driver must be filed prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.  If the case is settled with the insurance company, NO lawsuit is filed.