The provisions of this chapter requiring the deposit of proof of financial responsibility for the future, subject to certain exemptions, shall apply with respect to persons who have been convicted of or forfeited bail for certain offenses under motor vehicle laws, or who have failed to pay judgments upon causes of action arising out of ownership, maintenance or use of vehicles of a type subject to registration under the laws of this state, or who having driven or owned a vehicle involved in an accident are required to deposit security under the provisions of RCW 46.29.070.