What happens to your silencer after you die depends on how it’s registered. If you registered your silencer through an NFA gun trust, after your death, the suppressor goes to your co-trustee(s), or if they are also deceased, to the beneficiary.
If you registered as an individual, you need to declare who the silencer will be passed on to in your will. After your death, there will be a free transfer to your beneficiary, and they will have to complete similar paperwork you complete, namely an ATF Form 5.
If absolutely no one wants the silencer or is eligible to own it after your death, then the silencer may be turned over to the ATF and destroyed. But even then, a dealer may still be willing to take the silencer and resell it.