Car Accident (No Insurance) : Can the other driver ask me for more money after insurance will possible paid them?

Car Accident (No Insurance) : Can the other driver ask me for more money after insurance will possible paid them?

I was involved in a multi-car accident where I rear-ended the cars in front of me. The middle car, which had the most damage, they only have third party insurance, and I do not have insurance myself.

The owner of the middle car says they will claim through Budget Direct under their “Recovery Cover for No Fault Accident” ( which claim number doesn't want to share with me ) because we haven’t been able to reach an agreement regarding the amount they are asking me to pay. They have not provided invoices or proof of expenses.

My question is: if their insurance will possible pay them around $5,000 ( as he mentioned), can they also personally ask me for an additional $6,000? Or will the insurance company later contact me directly to recover the $5,000 they already paid out to them? Cause I don't think it is fair to pay for 11k for a car that does not value that.