You missed your insurance payment by two days had an accident that was not your fault is the other party pay for damages to your car through their insurance?

If you are truly not At Fault and the other insurance company is admitting liability then you should have no problem. As a side note I have heard of periodic rumblings that some states may enact a "pay to play" law. This would mean that even the "not at fault" party in an accident would have to have a valid insurance policy at the time of the accident in order to receive payment from the "at fault" driver's policy.