No, not legally. Here is the explanation why.
An entry visa to Russia is processed by the Russian consulates in foreign countries. No entity in Russia can issue a Russian visa.
Sometimes people think it a good idea to send their passport from Russia to their country via FedEx and have the consulate or a visa expediting agency send back the new visa once it is ready. Indeed, this would be the worst possible option to take because in such a case your new visa will be invalid as you will not have crossed the Russian border with this visa and obtained a stamp in your passport.
What with one visa expired and the other, invalid, a foreigner founds himself in a most difficult situation. The only thing he can do is to obtain an exit visa (which is a really complicated procedure) and leave the country directly.