What happens to your suppressed firearm when you die?

Factual Questions
1

People often leave gun to people in their wills. In the US, you can buy a suppressor for a pistol or rifle by paying a fee and having a background check. What happens to the gun or suppressor if you die? Can you leave it to someone else? Is there any provision where the authorities (BATF?) could hold it long enough to allow the relative to get licensed, is it confiscated and never seen again, or confiscated and sold and the money given to the heir?

I’m assuming the suppressor is integrated, since that would be more of an investment that someone may want to pass on, and a non-integrated suppressor would be treated separately from the gun.

2

Your heir fills out an ATF Form 5 and sends it to the ATF along with a death certificate. The firearm is transferred to the new beneficiary tax-free. The person must be eligible to possess the firearm. Otherwise it must be sold, surrendered (to the ATF), or destroyed.

There are also other ways which require more prep work before the death, but probable make things easier in the long run. Things like purchasing all the Title II weapons via a “corporation” and then just transferring the corporation after death. This also allows you to sell or transfer entire collections without tons and tons of Form 4s.