A lot of people don't this but Obama actually made it easier for legal immigrants to buy guns by removing the proof of 90 residency requirement. This happened around 2012 or 2013. Prior to that, legal immigrants were required to show proof of legal status and documentation showing they had been living in the US for at least 90 days. They could do so by showing things like utility bills or lease agreements.
Because Obama was not known for his pro-gun attitudes, I can only imagine that the move also made it easier for illegal immigrants to steal these weapons from relatives/friends who purchased them legally.