What will happen if the abuser tries to buy a gun when s/he isn't supposed to?
Before purchasing a gun from a licensed firearm dealer, all buyers must undergo a criminal background check that is processed through the National Instant Criminal Background Check System (NICS). If the abuser has a qualifying protection order against him/her, or has been convicted of a felony or domestic violence misdemeanor in any state, those records should be in the NICS, which should prevent the abuser from buying a gun. Not all states have automated record keeping systems, making it more difficult to process the criminal background check, and some criminals and abusers do slip through the system. Also, it is important to know that background checks are not required for private and online gun sales.
If the abuser is able to purchase a gun and you believe that s/he should not be able to have one under the law, you can alert the police, and ask that his/her gun be taken away and perhaps the police will investigate. Generally, it is not a good idea to assume that because the abuser was able to buy a gun, it is legal for him/her to have one.