A pedestrian mall established or to be established pursuant to this part may be so improved either concurrently with the proceedings taken under this part for the establishment of the pedestrian mall or at any time subsequent to the establishment of the city mall, but no contract for the work or improvement shall be awarded until moneys have been fully provided for the payment of all claims allowed pursuant to Section 11310 and for the payment of all damages and compensation, if any, awarded in any action or actions brought pursuant to Chapter 5 (commencing at Section 11400) hereof.