(a) If, when the cause of action accrues against a person, he or she is out of the state, the action may be commenced within the times herein limited, after his or her coming into or return to the state; and if, after the cause of action accrues, he or she departs from and resides out of the state, the time of his or her absence is no part of the time limited for the commencement of the action.
     (b) For purposes of subsection (a) of this Section no person shall be considered to be out of the State or to have departed from the State or to reside outside of the State during any period when he or she is subject to the jurisdiction of the courts of this State with respect to that cause of action pursuant to Sections 2-208 and 2-209 of this Act, Section 10-301 of “The Illinois Vehicle Code”, Section 5.25 of the “Business Corporation Act of 1983″, or any other statute authorizing service of process which would subject that person to the jurisdiction of the courts of this State. If a person files an action in a court of this State and attempts to secure service of process upon a defendant pursuant to a statute referred to in the preceding sentence, but does not obtain service of process upon such defendant, such defendant shall not be considered to be subject to the jurisdiction of the courts of this State at the time such action was filed, for purposes of the preceding sentence of this section. This subsection (b) of Section 13-208 of this Act shall apply only to actions commenced after October 1, 1973.