Safe Deposit boxes are protected, but where is not absolutely clear based on the SCRA. I place protections under Sect 3958 while I have heard some classify it as a lease under Sect. 3952. The latter states;
"After a servicemember enters military service, a contract by the servicemember for--
(A) the purchase of real or personal property (including a motor vehicle); or
(B) the lease or bailment of such property,
may not be rescinded or terminated for a breach of terms of the contract occurring before or during that person's military service, nor may the property be repossessed for such breach without a court order."
I do not see a safe deposit box as real or personal property even though it is considered a lease agreement.
Sect 3958 is protection against enforcement of a storage lien. This states, "A person holding a lien on the property or effects of a servicemember may not, during any period of military service of the servicemember and for 90 days thereafter, foreclose or enforce any lien on such property or effects without a court order granted before foreclosure or enforcement."
The bank may "lease" a safe deposit box and if the rental fee is not paid the bank may claim a storage lien on the property if your agreement so states. In other cases the box may be deemed abandoned and the contents escheated to the state according to state laws. I am not an expert in all the states laws and have read in some cases either of these scenarios.
As to your specific question, protection against a storage lien is automatic. It covers property of the servicemember. It doesn't say the servicemember has to be the lessor. This is important. It is a misdemeanor to knowingly take an action contrary to Sect. 3958, or attempt to do so. A person could be fined under Title 18 or imprisoned for not more than one year, or both for such an offense. Is it realistic to say that the contents of a safe deposit box must first have ownership verification prior to disposal? I think in most cases, unless there is compelling evidence to the contrary, you can assume the lessor is the owner. If your lessor is a servicemember, verifiable on the DMDC SCRA database, they are protected during military service and for 90 days after.
The DMDC's MLA database includes registered dependents of servicemembers. The SCRA database does not. You could check that MLA database if allowed, and then assume the property in the box could be owned by the servicemember and therefore be protected but there doesn't appear to be an obligation to do so, nor is a dependent clearly shown as a protected person under Sect 3958. It is the contents of the box, when owned by a servicemember, that are protected. If you can verify ownership, then you could drill or not drill.
To add to an already lengthy answer, once the bank drills it follows approved procedures to inventory and hold the property. Technically it has not sold or liquidated anything, it simply moved it from a jointly controlled box to one solely under the bank's control. The servicemember could still gain access to their property. Under state laws if the bank escheats the property to the state, a savvy attorney may be able to demonstrate the bank followed applicable law and turned the property over to the state. This is different than disposing or selling the property. The clearest evidence of a violation would be the sale or disposal of the property and that is rarely in the banks procedures unless the state refuses to accept whatever the property is and the bank does not keep it or converts it to cash, as an example, for past due fees.