Can a party issue a subpoena after discovery closes? No.
Rule 45 subpoenas “are subject to the same scheduling orders and deadlines as other forms of discovery.” William W. Schwarzer, California Practice Guide: Federal Civil Procedure before Trial, 11-308 (2013) (citing Marvin Lumber & Cedar Co. v. PPG Indus., Inc., 177 F.R.D. 443, 444 (D. Minn. 1997)). “[W]hen a plaintiff, as here, is aware of the existence of documents before the discovery cutoff date and issues discovery requests including subpoenas after the discovery deadline has passed, then the subpoenas and discovery requests should be denied. McNerney v. Archer Daniels Midland Co., 164 F.R.D. 584, 588 (W.D.N.Y. 1995).
If a party could evade discovery deadlines to continue to conduct third-party discovery until the time of trial, the universe of documents relevant to the case would never be settled prior to trial. This would defeat the purpose of the case management procedures detailed in the Federal Rules, increase the cost of litigation, impede settlement prospects, make trial preparation unwieldy, and wreak havoc on trial schedules.
Muench Photography, Inc. v. Pearson Educ., Inc., 2013 U.S. Dist. LEXIS 124064, 3 (N.D. Cal. Aug. 29, 2013).