IfI was driving someone else’s car and caused an accident, what amI liable for if the car I was driving wasinsured but I was not?

DO NOT sign anything.  Most auto insurance polices have what is known as  "permissive use" provision in their policy which gives full or limited coverage to someone who drives an insured vehicle with permission of the owner.  Did the owner report the accident?  They need to to make sure that the coverage is in effect and to advise them that you had permission.  Included with the payment on the premiums is an understanding that the drivers driving with permission will be "indemnified" i.e., covered and defended in a lawsuit.  You will be required to give them your complete cooperation which includes a statement now and whatever is necessary in defending your case.  Good luck.

NEVER sign an agreement that you are liable for all costs--that is an open-ended committment to pay anything, in any amount, traceable to the accident! That is the as bad as the worst outcome you could come to from being sued, even if you lost completely, so why do it?

If you are fault--which you probably are; the rear-driver in a collision like this is usually held to be at fault--the other party may collect his property damages; lost wages (if he took time off); other out-of-pocket (like towing); medical costs (if injured); and pain and suffering (if badly injured). However, not only must be fault be established, but these claims must be substantiated--i.e there must be evidence of them.

In a case like this, he could claim against the insurance of the car you were driving, or if they don't think they should pay, he'd have to sue the car's owner and they would defend under the policy; and/or he may sue the driver. (In a lawsuit, you may proceed against any at-fault parties.) Even if the insurer does pay, the insurance company may in turn sue you to recover your payments. So there is a good chance you will be sued by some party for damages  resulting from the accident, as described above.

Once and if you're sued, there will be a hard number that you can look at and evaluate whether to accept it and pay; whether to defend yourself in court; or whether to try to negotiate a somewhat better number to pay. Never simply agree to open-ended liability, and if sued--and if it's for more than a few hundred dollars--retain an attorney. If someone is basically just trying to get their deductible back (say, $500 -$1,000), you may wish to consider paying or settling to avoid the costs of defending yourself.