As @mzu already said, there are a lot of checks on borders in Russia, most of them are being made by passport controls, not the customs. Customs do the checks fir luggage - are there too many cash, are there some items prohibited from moving outside the Russia (such as paintings or rare items), are there drugs, etc.
Neither border control nor customs will check one's financial situation, because it's the point of interest for other country to check incoming people, and sums per day are different in different countries. The most popular case to get some funds for border control is that if one's who want to get outside the Russia has an unpaid bill, like taxes, driver fee, etc. If such sum is over
10000 RUR (about
$200), one could be stopped on border. However, if bill are paid (it can be done tight on border via electronic payments) one could continue theor trip without any problem.
So, basically if you'd have been said that someone need money for going through a border checks, the most probable scenario is that you're a target of scam. Do not send money, try to get back to Russia to see the person and resolve the situation with direct involvement.