Not quite the number is growing and according to Itar reports Ukrainian border agents are promising families leaving that they will never be let back in from Russia confirming that Ukrainian armed forces are expected to keep up shelling urban areas in the South East forcing out as many civilians as possible from a region supporting rights for the Russian speaking community.  About 20,000 women and children from southeastern Ukraine have crossed the Ukrainian-Russian border to the Rostov Region in the last three days. Over the last day 7,335 Ukrainian citizens entered the Rostov Region, the regional government said on Monday.On June 6, more than 12,000 Ukrainian residents were reported to arrive in Russia. After leaving cities and towns in the southeast, which are in the zone of fighting, most of the people move farther via Rostov. Some remain in temporary accommodation centres prepared by the Rostov region's authorities for refugees." (Article here)
Given the number and to ease the pressure on the local economies of the regions close to the Ukrainian border, check but think I did email u an article related to President Putin speaking of Ukrainian workers crossing the border daily to  fill jobs in Russia to be reconsidered making me wonder whether these well paying positions can be filled by the refugees if accommodation can be found moving north along the border with Ukraine for all these families.< /span>