W jezyku prawniczym "bond" znaczy "poreczenie", "gwarancja", "kaucja" itp., ale w tym przypadku moze najogolniejsze byloby "zabezpieczenie", choc - wolna wola, gdyz w Polsce niczego takiego nie ma przy okazji postepowania spadkowego.

Mechanizm wyjasniaja takie np. strony:

Q. Suppose my parents have only a very small estate. Is there any way to simplify the whole process.
Nearly every state allows for a streamlined administration procedure if an estate is small enough. In Florida, for example, estates that do not exceed $25,000 are eligible for "Summary Administration" rather than "Formal Administration" and the former can typically be accomplished without a lawyer. In New York the maximum limit for "small estate" treatment is $10,000. If an estate is within that limit, an eligible administrator can simply file an affidavit along with a death certificate to the Surrogate's Court, and the court clerk will issue a short form certificate of authority to act. No other proceedings or citations are required and the filing of a bond is also not necessary.
http://www.counselornet.com/emhesq/emhesqtax.shtml


Prerequisites to granting application.
Before granting
such application, the court shall require compliance with sub. (5)
and the filing of a bond by the foreign representative or of an addi-
tional bond for the protection of the estate and all interested per-
sons unless the court finds that the bond given under sub. (4) by
the local and foreign representative is sufficient.
www.legis.state.wi.us/statutes/01Stat0868.pdf

Hope that helps,

Jacek