Whenever any drainage district has been organized, established and created since January 1st, 1911, and extending to January 1st, 1921, in the manner provided by law, and the board of commissioners of such district have been authorized to proceed with the work of constructing a system of drainage for such district in the manner provided by law and have begun such work and expended the whole, or the major portion of the estimated cost of such improvement, and it shall have appeared to such board of commissioners that such improvement could not be completed within the estimated cost thereof so as to produce the benefits to the lands of the district found by the jury to be benefited by the proposed improvement without expending a greater sum than the estimated cost of such improvement and that the benefits which would actually accrue to the lands of the district would be sufficient to warrant the increased expenditure necessary to complete the improvement, and such board of commissioners shall have incurred indebtedness in the name of the district to such an amount as would complete the authorized system of drainage for the benefit of the lands of the district found by the jury to be benefited by the proposed improvement, and issued the warrants of the district to cover the additional cost of completing such improvement all warrants heretofore issued for such purposes are hereby declared to be valid and legal obligations of the district so issuing the same.