The Collaborative International Dictionary of English v.0.48:

Trustee process \Trus*tee" proc"ess\ (Law)
   The process of attachment by garnishment. [U. S.]
   [Webster 1913 Suppl.]

The Collaborative International Dictionary of English v.0.48:

Trustee \Trus*tee"\, n. (Law)
   A person to whom property is legally committed in trust, to
   be applied either for the benefit of specified individuals,
   or for public uses; one who is intrusted with property for
   the benefit of another; also, a person in whose hands the
   effects of another are attached in a trustee process.
   [1913 Webster]

   Trustee process (Law), a process by which a creditor may
      attach his debtor's goods, effects, and credits, in the
      hands of a third person; -- called, in some States, the
      process of foreign attachment, garnishment, or
      factorizing process. [U. S.]
      [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

TRUSTEE PROCESS, practice. In Massachusetts, this is a process given by
statute, in imitation of the foreign attachment of the English law.
     2. By this process, a creditor may attach any property or credits of
his debtor in the hands of a third person. This third person is, in the
English law, called the garnishee; in Massachusetts, he is the trustee.
White's Dig. tit. 148. Vide Attachment.